What do you need to know to master cross-browser and adaptive layout?

Question

Layout

Good afternoon!
I decided to upgrade my layout skills and therefore began to actively google cross-browser and adaptive layout.
To my surprise, in terms of cross-browser compatibility, I did not find anything normal later in 2014. The
question arose: did cross-browser compatibility come to naught?
If not, then please throw materials on it.
Also, advise what to see / read on the adaptive.
Thanks in advance )