I've been using Typescript for a while and have used a lot of frameworks for it, and some lack of frameworks (one of my earliest Typescript projects was a large conversion of an enterprise JS code base consisting of a mixture of JQuery 1.x, Backbone, and Knockout code). These days I've got one big project in Aurelia (which I'm not entirely thrilled with sometimes) and another in Cycle.js (which is quite cool and I'm using TSX there even).

I'm actually using it for the app logic/container in a riot.js app. Libraries like React/Riot/Vue are happy just being views in your Model-View-Whatever.

Angular is another story.

React, AngularJS v1, basically everything that more than 100 lines of js code.

We use both Backbone.js and React.