Quaternionic plurisubharmonic functions and their applications to convexity

The paper is a survey of the recent theory of plurisubharmonic functions of quaternionic variables, together with its applications to the theory of valuations on convex sets and HKT-geometry (Hyper-Kähler with Torsion). The exposition follows the papers [4, 5, 7] by the author and [8] by Verbitsky and the author.