Microsoft CEO Satya Nadella. Business Insider When 2015 kicked off, Microsoft was best known for its failures.

Sure, Satya Nadella won some cautious optimism in his first year as CEO with bold moves like releasing Microsoft Office for iPad and Android, embracing Linux, and buying Mojang and its smash-hit game "Minecraft" for $2.5 billion.

But Microsoft is best known for its Windows operating system. And Windows 8.1, then the current version, was not loved.

Fortunately for Nadella, Microsoft, and PC owners everywhere, though, 2015 was the year that Microsoft turned Windows around.

Announced in January, Windows 10 brought lots of people — including myself — back to the Windows fold. It's a solid operating system that represents a return to form, and it's mostly positive.

But Microsoft shouldn't rest on its laurels. The hard part is still ahead.

Windows 10

Microsoft kicked off 2015 with an event formally introducing Windows 10, skipping Windows 9. It was pitched as a huge update a long time in the making.

Windows 7, which remains the most popular PC operating system in the world six years after its launch, isn't great for the new, touch-based future in which we find ourselves.

Windows 8, by comparison, was a huge flop. It tried to balance touch-friendliness and the emergent app-store economy with the classic Windows approach, and ended up doing neither very well. Windows 8.1 tried to fix many of the most glaring issues, but the damage was done.

But this year's Windows 10 seems to have finally hit the sweet spot. It's a pleasure to use on a tablet like the flagship Microsoft Surface Pro 4, but it also has enough of that familiar Windows feeling that Windows 7 users won't be totally disoriented.

Better yet, Microsoft is making Windows 10 a free upgrade for Windows 7 and 8 users for its first year of availability.

A Microsoft Surface Pro 4 running Windows 10. Microsoft

So far, users have responded positively, with Microsoft reporting over 120 million Windows 10 installations since its official July 2015 release.

In a more forward-looking sense, too, Microsoft is pushing the Windows Store app market, a place where developers can sell software that runs on any Windows 10 device, from laptops to tablets to funky futuristic holographic goggles.

In November, the Xbox One got an update that added a version of Windows 10 at the core, paving the way toward making the video-game console a key part of the Windows family.

In fact, Microsoft CEO Satya Nadella says that he sees the Xbox One as the center of the company's smart-home strategy, saying that the Xbox One is "just another Windows computer." With Windows 10, everything in the world is exactly the same.

But the upgrade cycle hasn't exactly gone off without a hitch, thanks to privacy concerns and some strong-arm tactics to encourage upgrading. Generally speaking, though, people seem to love it. Slowly but surely, it's erasing or at least easing the bad vibes engendered by Windows 8.1.

The hard part

OK, so pats on the back all around. But Microsoft has one more huge disaster to fix, and it's a doozy: Smartphones, a field where Microsoft's position is so dire that some analysts have given up on it entirely.

While Microsoft Windows 10 is arguably the best Windows ever, Windows itself matters less with each passing day — without a viable stake in the smartphone market, it's being left behind in a massive shift, even as competitive pressure mounts.

In smartphones, Microsoft's global-market share hovers around 3%. For comparison, Google Android is the most popular smartphone operating system in the world, making it the most common operating system in the world, full stop.

Apple's iOS is in solid second place, and has helped turn the iPhone into a massive business. Apple's iPhone revenue for the last four quarters was greater than Microsoft's total revenue — or the revenue of any other single tech company.

Microsoft Lumia 950 phone running Windows 10 Mobile. Microsoft

It's a tough nut to crack. Smartphones live and die based on the apps available for them. And while Microsoft has made some encouraging partnerships with the likes of Facebook and Uber, the new Windows 10 Mobile just can't go app-for-app with an iPhone or Android phone.

It creates the proverbial vicious circle: Nobody buys Windows phones because there are no apps, and there are no apps because not enough people have Windows phones to make it worth a developer's time.

Meanwhile, Google and Apple are slowly but surely positioning their newest Android and iOS tablets as laptop replacements. The not-so-subtle subtext there is that these tech rivals think their operating systems can replace Windows, too.

The heat is on.

The rumor is that Microsoft is announcing a new killer phone next year that could change everything. And if Nadella can pull out a turnaround on this front, it would be one for the history books.