Ramsey theory on infinite structures aims for analogues of the infinite Ramsey theorem on structures such as the Rado graph, Henson graphs, the rationals, and Fra\"{i}ss\'{e} structures in general. It further seeks analogues of the Galvin-Prikry and Ellentuck theorems for such structures. We present an introduction to Ramsey theory on infinite structures and an overview of the current state of the art. This will include set theoretic and purely combinatorial methods.
