In the past two decades there has been intense interest in probabilistic aspects of finite groups. Moreover, probabilistic methods were instrumental in proving group-theoretic results, most notably in finite simple groups (with connections to other areas: combinatorics, geometry, computer science, etc).
I will describe some of the main developments and achievements in this area, and show how the probabilistic approach led to proofs of various challenging conjectures by Dixon, Babai, Cameron, Ore, Gowers and Viola. The talk will be accessible to a wide audience.
