Two-dimensional (2D) semiconductor nanocrystals display unconventional physical and opto-electronic properties due to their ultrathin and unique electronic structures. Since the success of Cd-based photoemissive nanocrystals, the development of sustainable and low-cost nanocrystals with enhanced electronic and physical properties has become a central research theme. In this context, copper-based semiconductor 2D nanocrystals, the cost-effective and eco-friendly alternative, exhibit unique plasmonic resonance, transport properties, and high ionic conductivity beneficial for sensing, energy storage, conversion, and catalytic applications. This review summarizes recent progress in the colloidal synthesis, growth mechanisms, properties, and applications of 2D copper-based nanostructures with tunable compositions, dimensions, and crystal phases. We highlight the growth mechanisms concerning their shape evolution in two dimensions. We analyse the effectiveness of cation exchange as a tool to synthesize multinary nanocrystals. Based on the preparation of Cu-based chalcogenide and non-chalcogenide compositions, we discuss synthesis control achieved via colloidal approaches to allow dimension tunability, phase engineering, and plasmonic and thermoelectric property optimization. Furthermore, their potential in various applications of catalysis, energy storage, and sensing is reviewed. Finally, we address the current challenges associated with 2D Cu-based nanocrystal development and provide an outlook pertaining to unexplored research areas.