Toric topology is an active area at the intersection of topology, algebraic geometry,
differential topology, and combinatorics. Roughly speaking, a quasitoric manifold is
a complex manifold equipped with a torus action whose orbit space is a simple
convex polytope. This talk will introduce the basic ideas of toric topology and
explore algebraic-topological aspects of these manifolds through examples, with
emphasis on their cohomology rings and homotopy groups. I will also discuss open
problems, particularly rigidity conjectures. Time permitting, I will briefly overview
stable splittings of certain toric spaces related to quasitoric manifolds.
