  The goal of this article is to present a survey of the recent theory of
plurisubharmonic functions of quaternionic variables, and its applications to
theory of valuations on convex sets and HKT-geometry (HyperK\"ahler with
Torsion). The exposition follows the articles math.CV/0104209, math.CV/0208005,
math.MG/0401219 by the author and math.CV/0510140 by M. Verbitsky and the
author.
