Because of the specific properties including HOMO-LUMO electronic transition, size-dependent fluorescent emission, and intense light absorption, metal nanoclusters (NCs) have been considered to be one of the most competitive color conversion materials in light-emitting diodes (LEDs). However, the monotonous emission color and the low emission stability and intensity of individual metal NCs strongly limit their universal application. Inspired by the concept of "aggregation-induced emission" (AIE), the utilization of highly ordered metal NC assemblies opens a door to resolve these problems. After self-assembly, the emission stability and intensity of metal NC assemblies are enhanced. At the same time, the emission color of metal NC assemblies become tunable. We termed this process as self-assembly driven AIE of metal NCs. In this review, we use Cu NCs as the example to convey the concept that the compact and ordered arrangement can efficiently improve the metal NCs' emission stability, tunability, and intensity. We first introduce the synthesis of 2D Cu NC self-assemblies and their emissions. We further summarize some of the factors that can affect the emissions of 2D Cu NC self-assemblies. We then discuss the utilization of 2D Cu NC self-assemblies as color conversion materials for LEDs. At last, we outline current challenges and our perspectives on the development of this area.