  Arithmetical properties of a finite group are properties of the group which
are defined by its arithmetical parameters such as the order of the group, the
element orders and so on. In this paper, we discuss a number of results on
arithmetical properties of finite groups and characterizations of finite groups
by their arithmetical parameters obtained recently. This paper is based on the
talk by the author given in frame of (WM)^2 - World Meeting for Women in
Mathematics-2022.
