Much of the theory of Distributed systems is published at Principles of Distributed Systems (PODC). However, a lot of emphasis there is on the asynchronous model. Results that hold for the asynchronous model generally hold for other models. The main point a layman needs to know about the asynchronous model is that a slow node cannot be distinguished from a dead node.
Implementers of distributed systems will generally ignore most results on the asynchronous model. A slow node might as well be a dead node, so we can use heartbeats and timeouts to exclude these nodes. Typically, robust distributed systems in industry will follow some form of partially synchronous model, adapted to the type of environment it works in: LAN on baremetal => reliable, almost synchronous when not overloaded; WAN (Internet) => as close to the asynchronous model as is practical.