MS only bought the mobile arm of Nokia; the rest of Nokia still remains a wholly separate entity.

Microsoft did nothing with Nokia mobile because Microsoft’s mobile strategy was just not well-formed. It was one of the last deals that Ballmer made as CEO too, so Nadella’s promotion meant a change in strategy (his new direction has been quite successful).

Once they bought Nokia, Nokia was tied to the success of Windows Phone, which was already on life-support, and just couldn’t get traction. (They also did feature phones, which kept the mobile division in business, but that side of the business was not a focus for Microsoft). Their last few smartphones were apparently quite decent (especially the Lumia 950, which I know its fans clung to), but was just too-little-too-late.

The Nokia brand still puts out phones though: Microsoft sold the remains for a song to a small company in Finland, HMD (which might license the name from the main Nokia company itself as well), after writing off the bulk of their original purchase price.

HMD’s strategy has since been lower priced (hopefully higher volume) products, since they do not have the same resources as the bigger players. Still, they have carved out a niche for themselves, keeping the feature phones going (including w 4G) and some mid-range Android smartphones too. Not going to take top prize anywhere, but they seem to do alright.

(I used Nokia feature phones for years; the Series 40 platform was great, but it eventually had to give way to smartphones.)