In this talk, we explore some basic notions related to the (algebraic) dynamics of endomorphisms of projective varieties over a field, such as the iterated image and the dynamical Stein factorization. We then turn to the so-called bounded endomorphisms, having the property that all iterates remain within a finite union of connected components of the endomorphism scheme. These endomorphisms exhibit accessible dynamics, and one key ingredient in understanding them is a class of algebraic groups known as monothetic (i.e. having a dense cyclic subgroup).