The so-called retail apocalypse has laid waste to a number of well-known brands.

Chains that were once strong have struggled, and a shocking number of them sit on the verge of bankruptcy. You can blame the internet, but it's more than just some shoppers shifting their business online. For the retailers that have suffered, it's more about how they ignored the change.

Of course, not every retailer has struggled. One, Amazon (NASDAQ:AMZN), has been the source of the disruption. The digital leader has led the charge to make online shopping convenient by pushing faster delivery and constantly evolving its technology.

Amazon is not the only retailer succeeding, though. Wal-Mart (NYSE:WMT) has righted its ship after a series of early struggles, and Costco (NASDAQ:COST) has shown that a market exists for brick-and-mortar stores as long as they offer the right experience for shoppers.

Amazon is king

It's fair to credit Amazon for leading the digital revolution. The company has changed expectations for how online shopping works. By making two-day delivery a standard and pushing even faster methods of getting goods in customer's hands, the company has removed one clear barrier to digital shopping.

Shopping on Amazon.com may not provide the instant gratification that going to a store does, but it comes with a lot less hassle. That has led the company to stellar and steady growth, including a 23% increase in net sales in Q1 from $29.1 billion in 2016 to $35.7 billion in Q1 2017.

Of course, Amazon no longer derives all of its revenue as a retailer, but those segments still dominate its business and are growing rapidly. North American retail sales grew by 24% in Q1, while international e-commerce sales rose by 16%.

Amazon has steadily grown its Prime membership base, hitting 80 million members in the United States alone in April according to data from Consumer Intelligence Research Partners (CIRP). That's a huge base of loyal customers that the online retailer should be able to keep building as it grows its dominance around the world.

A Wal-Mart workers picks a digital order.

Wal-Mart has been integrating its digital operations with its stores. Image source: Wal-Mart.

Wal-Mart has mounted a comeback

For a few years Wal-Mart struggled to integrate its massive network of physical stores and its fledgling digital operations. The two segments of the company did not work well together and did not support each other.

That changed in August when the company spent $3.3 billion buying Jet.com and put its entrepreneurial CEO Marc Lore in charge of its online operations. Since taking charge, Lore has led a cultural shift. He has pushed the idea that physical and digital must work together to create a seamless omnichannel experience for shoppers.

So far that approach has worked. In Q1, the company grew U.S. comparable-store sales by 1.4% while its online sales jumped by 63%. Credit Lore for that, as he made immediate bold changes like offering free shipping on orders over $35 while working on longer-term projects to make ordering online and picking up in store easier.

Wal-Mart has work to do, but it has shown it can grow revenue by leveraging its store network alongside its digital operation. That's an edge over Amazon and one the company should be able to further exploit as it continues to deliver small in-store growth alongside significant digital gains.

Costco has a model that works

Unlike most retailers, Costco has not made any major changes since digital became a disruptive force. The company continued to build its warehouse clubs and rely on the fact that its stores offer destination shopping. Consumers may not want to leave their house as often for certain types of retail, but Costco's stores have been the exception.

That has been true because the company gives its members a reason to visit. Yes, the chain offers low prices, but it also delivers a sense of discovery. You never know what bargain may be awaiting you at a Costco and that gives consumers a reason to visit.

Most importantly, since Costco makes about 75% of its revenue from membership sales, the chain has been growing that metric. The chain steadily delivers a renewal rate near 90% across the globe. It finished its fiscal Q2 with 37.5 million Gold Star members, up from 37.2 million at the end of the first quarter. Total accounts, CFO Richard Galanti noted during the earnings call, rose to 48.3 million from 47.9 million in the first quarter.

"Total card holders [were] 88.1 million at second quarter end, up from 87.3 million 12 weeks earlier," said Galanti, according to Seeking Alpha's transcript of the call (registration required). "As of Q2 end, our paid Executive Memberships stood at 17.9 million, which is an increase of about 200,000 from 12 weeks earlier, or about 17,000 additional per week."

Costco may not be the most exciting company on this list, but it has a model which resonates with consumers. The warehouse club should continue to grow and remain unimpacted by the forces which have hurt so many other retailers.

Daniel Kline has no position in any of the stocks mentioned. The Motley Fool owns shares of and recommends Amazon. The Motley Fool recommends Costco Wholesale. The Motley Fool has a disclosure policy.