Verlyn started it, as far as I am concerned. Sometime in 2000, my colleague started bringing his Mac laptop to our New York Times editorial board meetings. The rest of us would hover around the sleek white machine with the cool lighting radiating from it, wondering if Verlyn Klinkenborg could possibly be serious. Some of us had used Apples in college, sure, but everyone does crazy things in college.

Was an Apple really fit for a workplace? Verlyn assured us that it was no toy, and that his Mac could do all the things ours could—the mix of surfing, emailing, and pontificating that the gig entailed—without crashing as frequently as our PCs. Verlyn claimed that his Apple was not susceptible to those nasty viruses that plagued our land of “Wintel,” and I wanted to believe him. I too bought a Mac, and instantly felt cooler as a result.

Fast forward to 2015, and some days it feels like the novelty would be for someone at a meeting to take out a laptop that isn’t an Apple. And yet, somehow, the caché and cool factor remain. Apple has managed to walk the tightrope between ubiquity and coolness, attaining one without sacrificing the other.

The company just announced the most profitable quarter in U.S. corporate history, a three-month period in which it sold almost 75 million iPhones and 5.5 million Macs and made $18 billion. Tim Cook, Steve Jobs’ accessible and down-to-earth successor as CEO, couldn’t help himself on the earnings call, describing the quarter as “historic” and his company’s performance—selling on average 34,000 iPhones an hour, 24/7—as “hard to comprehend.” Apple is now the world’s most valuable company, with a stock market valuation of some $700 billion, and nearly $180 billion in cash on hand. The company’s online iTunes store counts a staggering 800 million active users.

What’s most astonishing, given those numbers, is that Apple is far less ubiquitous than you might think. It actually has plenty of room to grow. Indeed, it may only be getting started.

If you look at its existing product lines, Apple only truly dominates the tablet market. In the far more important (in terms of profit margins) phone and computer markets, Apple doesn’t lead the pack. The competing Android operating system runs more than two-thirds of the world’s smartphones. Apple ranks fifth worldwide in the number of computers sold, and third in the U.S., where its market share has been steadily creeping up toward the 15 percent mark. In both computers and phones, there is plenty of market share left for Apple to steal from others.

Apple’s growth strategy is impressively disciplined and patient. The company doesn’t slash prices or create subpar products to meet less affluent consumers in emerging markets halfway. Apple instead holds out its meticulously designed, pricier products as coveted trophies for new middle-class consumers. In much of the world, an Apple device has replaced the Louis Vuitton bag as the most tangible symbol that you have arrived. If you want to showcase your universal consumerist aspirations, head to one of those starkly modern Apple stores that are fast becoming landmarks in most global cities.

Not long ago, critics scoffed at Apple’s foray into China with its higher-priced devices (luxury items, really), predicting a rout. No one is scoffing now. In the last quarter, Apple’s iPhones outsold all other smartphones in China, as the company pulled in $16 billion in revenue. The world’s busiest Apple store is in Shanghai, and Cook made a point on the earnings call to say Apple intended to open 40 stores across China soon. Apple doesn’t chase foreign consumers, but rather waits for them to become affluent enough to afford its wares.

If Apple’s prowess is impressive when looking at its existing product lines, the company’s true potential becomes even harder to comprehend (as Cook might put it) when you consider that it is only starting to wade into an array of markets that it will likely revolutionize, and dominate, in short order. Apple Pay, its bid to become your all-encompassing cashless wallet, is off to a strong start. Fledgling Apple ventures like HomeKit, CarPlay, and iBeacon provide clues to Apple’s unstated, ultimate goal: providing you with one portal, or operating system, that links your Apple devices, your car, and your home. As the “Internet of Things” evolves from hype to reality, Apple will seek to hand you a remote control—to your entire life. The Apple Watch, coming this spring, will no doubt be central to this effort, possibly making the brand indispensable to consumers in even more ways, particularly in tracking their health and fitness.

As was true with past devices and services, Apple is hardly being a trailblazing pioneer. There are plenty of “smart watches” and digital wallet surrogates already out there, but Apple has a way of biding its time, learning from the mistakes of others, and then introducing a tweaked product or concept that will go mainstream, in part because it fits in so well within the broader Apple ecosystem.

People at Apple talk a lot about this notion of an ecosystem. The company isn’t mainly about the hardware or the software, but the interplay between the two. Earlier, this was one of the knocks against Apple, that Jobs obsessively controlled both hardware and software—creating a closed system to protect precious aesthetic sensibilities—to a point where the company was out of step with the more open and collaborative tech culture. Hardcore techies have always resented what they consider Apple’s heavy-handed efforts to create tidy, uniform, turnkey systems that resist hacking or excessive customization.

But a coherent ecosystem is exactly what your average consumer wants.

No other company is anywhere near being able to match Apple in providing us with such seamless curation of our lives. The Italian novelist Umberto Eco famously said in the 1990s that Apple was like Catholicism, in that its followers had to adhere to one way of doing things, while Microsoft (you could say Google nowadays) was more akin to Protestantism, which gave followers more latitude to reach their own conclusions and organize themselves accordingly. Apple is unique among Internet giants in getting consumers to pay top dollar for its goods and services, while other companies like Facebook and Google rely instead primarily on an advertising model to subsidize their interactions with consumers.

And so Apple’s prospects appear brighter than ever. Its own success would seem to be the only threat to a company that has billed itself as the scrappy underdog. After all, it was Apple who encouraged us to “think different” and launched its iconic first Mac in 1984 with a commercial celebrating the machine’s subversive ability to deliver us from an Orwellian “1984” collectivist nightmare.

Therein lies the company’s existential challenge: Can Apple remain cool if its products become the one indispensable means of controlling your life and communicating with others? Can it remain an aspirational brand once it’s within everyone’s reach? How distinctive can the world’s largest company, no matter what it does, ever be?

I reached out to Verlyn, who now teaches at Yale, to ask whether he’s still inhabiting the Apple ecosystem. He is, and his disgust at his pre-2000 Windows experience sounds as raw as it did when he first started proselytizing for the Mac. But he draws a line at the coming Apple Watch: “I’ve never worn a watch, and I can’t imagine starting now.”