Byzantine process is a process that --intentionally or not-- behaves arbitrarily (Byzantine failures include crash and omission failures). Considering message-passing systems, this paper presents communication and agreement abstractions that allow non-faulty processes to correctly cooperate, despite the uncertainty created by the net effect of asynchrony and Byzantine failures. The world is distributed. Consequently more and more applications are distributed, and the ''no Byzantine failure'' assumption is no longer reasonable. Hence, due to both the development of clouds and security requirements, such abstractions are becoming more and more important. The aim of this paper is to be a simple and homogeneous introduction to (a) communication and agreement abstractions, and (b) algorithms that implement these abstractions, in the context of asynchronous distributed message-passing systems where an a priori unknown subset of processes may exhibit Byzantine failures. To that end the paper presents existing abstractions and algorithms, and new ones. In this sense the paper has a mixed ''pedagogical/survey/research'' flavor.