Where can I read reviews of mathematical theories? I'm really enjoying the AMS column "What is ..." (http://arminstraub.com/math/what-is-column) and The Princeton Companion to Mathematics.
I am looking for something similar. I'd like to acquire some intuition behind different subjects and the general overview rather than digging into details and technical proofs.
I want to read more about the motivation, the greatest results and applications (inside and outside of mathematics). 
 A: An addendum to Alexandre's answer: I have noticed that in some "proceedings"  or "conference" volumes, the first article (or the introduction) is a very nice overview of the theory that is treated in the book. The same can be found in books with the title "on the occasion of the [age]-th birthday of [some big name in mathematics]".
A: On the popular level, there is an AMS feature column:
http://www.ams.org/samplings/feature-column/fc-current.cgi
and a series of 10 volumes "What's happening in mathematical sciences":
https://bookstore.ams.org/HAPPENING,
also by AMS.
On a higher level, there are journals which publish surveys, addressed to
the general audience of mathematicians: Bulletin of the AMS, Russian Math Surveys,
Sugaku expositions, Gazette des Mathematiciens, Expositiones Mathematicae, L’Enseignement Mathématique, and several other such journals.
A: Look for books with the word "Handbook" in the title.  These often contain well-written survey articles by leading experts.  The downside is that "Handbooks" tend to be rather expensive, but you may be able to find them in your library.
