Almost 20 years ago, a new company came on the scene promising to revolutionize the tedious and often frustrating chore of securing a restaurant reservation.

No more waiting on the phone and pleading with snooty receptionists. With just a few clicks of a mouse, a diner could secure a table at prime times in the hottest dining spots. Who you were or knew would no longer matter. Restaurants would benefit, too, handing off the job of juggling tables and recording reservations in a bulky book.

The company was called OpenTable, and, since its genesis in 1998, it has come to dominate the field it created. Today, it says it seats more than 23 million diners a month in 43,000 restaurants across the globe.

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Two decades on, though, the company faces a number of troubles that threaten that hold. Priceline, which now owns it, has written down the company’s value and said it is reducing investments in the system. A new crop of competitors is challenging OpenTable as never before, picking off the high-profile restaurants that are critical to attracting consumers, by offering better deals and newer technology.

And for all the diners they do seat, neither OpenTable nor its competitors have yet loosened the telephone’s grip on reservations, roughly two-thirds of which are still made by phone, according to Yelp, which once partnered with OpenTable and is now a rival.

This year, Table8, a reservation system started in 2013, folded, unable to raise additional funds to keep going. So far, none of the new services appear to be profitable.

“Everyone is fighting to win over the handful of top restaurants in each market — and then what?” said Jeff Jordan, a former chief executive of OpenTable who is now a venture capitalist. “It’s hard to see the endgame.”

Consumers continue to have fundamental gripes about these services: chiefly, that they offer few or no tables during the peak dining hours. They make it difficult to book tables for large or odd-numbered parties, which is why diners like Jeff Day, a marketing executive in Austin, Tex., keeps no reservation apps on his phone.

“My default way to make reservations is still to call,” he said, “I guess because my desire to speak to a human transcends the need to just make a reservation.”

His wife, Teresa, however, recently added one of the upstarts, Reserve, to her phone. “I think I’ve used OpenTable for 10 years, and it has a really good loyalty program that gives you points to use in restaurants or on Amazon,” she said. “But Reserve has better restaurants, places that are hipper, newer and just more desirable.”

Reserve has managed to attract those restaurants because, like many of other new reservation services, it is paying more attention to meeting their needs. After all, the restaurants are paying monthly fees for the service.

But winning over restaurateurs, many of whom have accumulated a long list of gripes against what they perceive as cookie-cutter approach to their reservation woes, is still a challenge.

“These kinds of technologies have been a boon for the diner,” said David Barber, an owner of Blue Hill in New York City and Blue Hill at Stone Barns in Westchester County. “But the idea that it’s delivered this great efficiency to the restaurant business is kind of a myth, especially for fine-dining restaurants.”

OpenTable is not just standing by as others invade its turf. While it has been slow to move in the past, last spring it upgraded its flagship GuestCenter package for restaurant managers, improving its ability to handle large parties and better juggle servers’ shifts, among other things.

Restaurateurs can now see what’s happening with their reservations in real time and even on their Apple Watch. And OpenTable offers consumers points that can earn benefits like access to special wine tastings or menus at various OpenTable restaurants.

“Competition for our business is not new,” said Scott Jampol, the company’s senior vice president for marketing. “It makes us faster and more innovative.”

Not all of that innovation has paid off. Last November, Priceline announced that it had written off $941 million of OpenTable’s value, after a rapid burst of investment to expand the service’s international offerings failed to produce the expected profits. The travel behemoth, which paid $2.6 billionfor OpenTable in 2014, also predicted a “material reduction in forecasted long-term financial results and a reduction in investment” in the business.

Leslie Cafferty, a Priceline spokeswoman, said OpenTable is profitable and bigger than it was then. She said Priceline had bought the company based on a strategic plan that was in place at the time but has since changed. “We’ve had some changes in leadership in OpenTable and in the Priceline Group,” Ms. Cafferty said. “When we got caught up and looked at where OpenTable was, it was basically different than when we bought it.”

Competitors have chipped away at OpenTable’s business. In July, it lost Le Bernardin and Augustine, two hard-to-book New York restaurants, to Resy, an elegant app-based reservation system started in 2014 by Ben Leventhal, a founder of Eater.

Resy, now used by roughly 1,000 restaurants in 80 cities across the country, has seated more than 25 million diners since its inception, and the number of meals served to those using its system quadrupled in the year that ended in May, Mr. Leventhal said.

“In fine dining, you have the cost of business going up, the notion of fine dining evolving rapidly, a lot of restaurants being forced to rethink their formats and business models,” he said. “That means you have to make sure every table is working for you, and restaurants are finally embracing technology that can help them do that.”

Many restaurants that use Resy, for instance, require diners making a reservation to enter a credit-card number, in an effort to discourage no-shows and cancellations; about 1 percent require a down payment. Resy follows up to remind diners when a reservation they made is imminent.

Users can also put themselves on a waiting list at some restaurants, which makes it much easier to ensure that all tables will be filled, since most cancellations happen within 24 hours before the reservation time. As a result, Resy says, it has brought no-shows down to under 4 percent on average; the usual rate is as much as 15 percent, the company said.

Perhaps the company’s biggest coup, though, was winning over Union Square Cafe when that perennially popular New York restaurant reopened in December. Danny Meyer, the founder of Union Square Hospitality Group, was on the OpenTable board for almost two decades and one of its best ambassadors.

In the mid-1990s, when Mr. Meyer was working to open his second restaurant, Gramercy Tavern, he tried starting a similar system himself. He didn’t even think about using it to allow customers to make reservations online; rather, it was to be an answer to a perennial problem.

“I was tired of this recurring problem we had in the restaurant, where people would always be yelling up and down the stairs, saying, ‘Who’s got the reservation book?’ ” Mr. Meyer said. “One time a fraternity brother of mine pulled a prank and took the book out of the restaurant entirely — it was not a nice prank.”

So when he opened Eleven Madison Park in 1998, OpenTable was taking the reservations. When Blue Smoke opened in 2002, the only way to make a reservation was via OpenTable; a phone line was discontinued. “I’ll never forget it,” Mr. Meyer said. “An online blog called Daily Candy announced that step and within hours, we had filled the entire restaurant for a month.”

But OpenTable had its limitations. Until recently, for instance, it would not link the reservation systems at the Union Square group’s restaurants. A free-spending diner who patronized Union Square Cafe for years could show up at Gramercy Tavern for the first time, and the host would not know him.

Mr. Meyer said that, to some extent, OpenTable had been criticized unfairly. After all, it still seats far more diners in restaurants like his than any other service, and serves all the Union Square group restaurants except Union Square Cafe and the new Martina, which doesn’t take reservations. Nonetheless, he said, “the latest round of assaults from start-ups looking to eat their lunch is more than they’ve ever faced before.”

The rivals have easily identified OpenTable’s Achilles’ heel: the fees it charges restaurants every time someone books a table using its system. For reservations made on OpenTable, the restaurant pays $1 for each diner. Even if reservations are made on the restaurant’s website, OpenTable charges 25 cents a diner. And if they don’t show up, the restaurant recoups none of those fees, several restaurateurs said. (OpenTable, however, says it charges fees only for guests who do show up.)

That galled Anjan Mitra, proprietor of Dosa, a popular Indian restaurant with locations in San Francisco and Oakland, Calif. Many of his diners are repeat customers, he said, coming two or three times a month and using OpenTable to make reservations.

“I don’t mind paying OpenTable for new customers, but OpenTable was charging me for customers I already had and knew well,” Mr. Mitra said.

He said he paid as much as $50,000 to OpenTable in fees on top of the $295 a month for use of its technology. “Consumers don’t know this,” Mr. Mitra said. “They just love the convenience, and I understand that.”

Dosa has switched to Yelp, which now offers several features to help restaurants manage their reservations — a surprising twist for a company that many restaurateurs love to hate for its sometimes-withering user reviews.

Yelp says more than 4,000 restaurants now use its service for reservations. The company doesn’t need to attract marquee dining spots to entice users, who are already coming to it for reviews, giving it a major advantage.

Yelp Reservations charges a restaurant $249 a month, and, in exchange, a reservations option is added to the top of its page on the Yelp app and website. “Many people planning to make a reservation for dinner are already opening Yelp to figure out where they want to go, and now they can see whether there’s a table waiting for them or not,” said Vishwas Prabhakara, the general manager of Yelp Reservations.

He said the flat-monthly-fee model used by most of the new reservation services helped discourage a restaurant practice that infuriates customers: holding back tables during prime hours. Some restaurants do that because they know they can fill the tables on their own at those times, and they like to seat valuable guests who show up at the last minute.

“There’s no incentive to hold tables back because you’re not having to pay for each reservation,” Mr. Prabhakara said.

Nick Kokonas, an owner of the Chicago restaurants Alinea and Next, said he helped found the online reservation system Tock in 2014 because he was frustrated with his own experience with OpenTable.

“People in the restaurant business have moved from fear of change to a recognition that OpenTable was built in 1998,” he said. “They haven’t really kept up innovation-wise, and part of that is because of the architecture of their technology.”

He said that, until this summer, OpenTable gave restaurants only “one blank box on the screen” to enter a wide range of information on a diner — such as dietary restrictions, preferred nights of the week and wines ordered — instead of separate fields that made it easy to see if a customer, say, has lactose intolerance.

“Not to be creepy, but instantaneous and easy-to-read customer data is the best way we have to give the customer the best service,” Mr. Kokonas said. “It lets us know that the last time you were here, you finished with a special spiced tea that you liked, and we can make that happen again and easily.”

Mr. Jampol of OpenTable said that his company also compiles piles of similar data on customers that restaurants could use — but that they rarely want it. “Restaurateurs have a lot of things to keep track of every day,” he said. “And as much as they say they want data, they’re often too busy to dive into it.”

Nonetheless, Mr. Kokonas and others see an opportunity to do it better. Tock, which was co-founded by Brian Fitzpatrick, a former Google engineer, spent roughly two years building its system, testing different components with restaurants and getting feedback. It is web-based rather than app-based, because that makes it easier for restaurants to log in and configure Tock to their needs.

Other new reservation services are also looking to please restaurants. Reserve has adopted an “open data model” that allows its restaurants to see what diners are looking for, and, since it tweaked it service in May, it is adding more than 100 restaurants a month (for a total of 850), said Peter Esmond, its vice president for customer success.

Say a potential customer is seeking a table for four at 7:30 p.m., and a restaurant is showing nothing available at that time. If it has a table available then that it has held back, it can quickly add it to its Reserve page in an effort to attract the booking.

Thus, more control over how reservations are made is put in the hands of restaurants, rather than the reservation app.

At Blue Hill, Reserve worked with Mr. Barber to tailor its product to his needs. And that, Mr. Barber said, is why a monolithic reservation titan like OpenTable may be a thing of the past.

“Trying to build ubiquitous software that will meet all the needs of high-, middle- and low-priced restaurants and make consumers happy, that’s a nightmare,” he said. “Having a baseline product that comes close to what OpenTable does and then allows some customization, that’s what the restaurant business wants — and then customers will really start to see the benefit of these things.”