Due to the advent of multicore machines, shared memory distributed computing models taking into account asynchrony and process crashes are becoming more and more important. This paper visits models for these systems and analyses their properties from a computability point of view. Among them, the base snapshot model and the iterated model are particularly investigated. The paper visits also several approaches that have been proposed to model failures (mainly the wait-free model and the adversary model) and gives also a look at the BG simulation. The aim of this survey is to help the reader to better understand the power and limits of distributed computing shared memory models.