Craft CMS and JS/MVVM frameworks
I am just starting out on a project using both Craft and Angular. I ran into an early issue because both Angular and Twig use the {{ }} braces, but that was quickly fixed by changing Angular’s settings like in this Stackover flow post.

As Christian noted in the comments, though, you could also use the {% verbatim %} tag to keep Craft from parsing Angular tags.

Aside from that, I haven't had issues since Craft gives you full frontend control and there are no CMS scripts on the frontend to worry about. And (so far) Craft's dynamic routes make it really quite easy to set up your templates, JSON, etc.