Toric varieties are fascinating objects that link algebraic geometry and convex geometry. They make an appearance in a wide range of seemingly disparate areas of mathematics. In this talk, I will discuss the role of projective toric varieties in one facet of topology called cobordism theory. Generally speaking, cobordism is an equivalence relation on smooth manifolds. After an introduction to projective toric varieties and cobordism, I will address the question of when an equivalence class in cobordism contains a projective toric variety, providing results in low dimensions. I will also discuss the role that toric varieties play in the algebraic structure on the set of these equivalence classes.