Dynamical Aspects of Sofic and Non-Sofic Groups

From their origin sofic groups have had a strong connection to topological dynamics in that it was shown that sofic groups are surjunctive - a dynamical notion. Later on, Lewis Bowen developed an entropy theory for sofic groups. This led to further extensions of classical dynamical notions like mean dimension to sofic groups. I will survey some of this history, and now that it has been shown that not all groups are sofic, I will also describe some dynamical results that are valid for all countable groups.