A toric vector bundle is a vector bundle over a toric variety equipped with a lift of the action action of the associated torus. Toric vector bundles were first classified by Kaneyama, and later by Klyachko using the data of decorated subspace arrangements. This description has been at the center of many interesting results and has enabled toric vector bundles to be a testing ground for the geometry of vector bundles over algebraic varieties. I'll review basics of toric geometry, along with Klyachko's classification, and then explain how moduli, spaces of global sections, and various notions of positivity look in this setting.