Anisotropic colloidal quasi-two-dimensional nanoplates (NPLs) hold great promise as functional materials due to their combination of low dimensional optoelectronic properties and versatility through colloidal synthesis. Recently, lead-halide perovskites have emerged as important optoelectronic materials with excellent efficiencies in photovoltaic and light-emitting applications. Here we report the synthesis of quantum confined all inorganic cesium lead halide nanoplates in the perovskite crystal structure that are also highly luminescent (PLQY 84%). The controllable self-assembly of nanoplates either into stacked columnar phases or crystallographic-oriented thin-sheet structures is demonstrated. The broad accessible emission range, high native quantum yields, and ease of self-assembly make perovskite NPLs an ideal platform for fundamental optoelectronic studies and the investigation of future devices.