This is the newest version of their architecture I've seen [0]. Compare to an overview from 2009 [1].
tl;dr StackOverflow's architecture is fairly simple and has done mostly vertical scaling (more powerful machines) and bare metal servers rather than virtual servers. They also realize their use patterns are read-heavy so there's a lot of caching and they take advantage of CDNs for static content which completely offloads that traffic off their main servers.
[0] https://nickcraver.com/blog/2016/02/17/stack-overflow-the-ar...
[1] http://highscalability.com/stack-overflow-architecture
