This review summaries the optical properties, recent progress in synthesis, and a range of applications of luminescent Cu-based ternary or quaternary quantum dots (QDs). We first present the unique optical properties of the Cu-based multicomponent QDs, regarding their emission mechanism, high photoluminescent quantum yields (PLQYs), size-dependent bandgap, composition-dependent bandgap, broad emission range, large Stokes’ shift, and long photoluminescent (PL) lifetimes. Huge progress has taken place in this area over the past years, via detailed experimenting and modelling, giving a much more complete understanding of these nanomaterials and enabling the means to control and therefore take full advantage of their important properties. We then fully explore the techniques to prepare the various types of Cu-based ternary or quaternary QDs (including anisotropic nanocrystals (NCs), polytypic NCs, and spherical, nanorod and tetrapod core/shell heterostructures) are introduced in subsequent sections. To date, various strategies have been employed to understand and control the QDs distinct and new morphologies, with the recent development of Cu-based nanorod and tetrapod structure synthesis highlighted. Next, we summarize a series of applications of these luminescent Cu-based anisotropic and core/shell heterostructures, covering luminescent solar concentrators (LSCs), bioimaging and light emitting diodes (LEDs). Finally, we provide perspectives on the overall current status, challenges, and future directions in this field. The confluence of advances in the synthesis, properties, and applications of these Cu-based QDs presents an important opportunity to a wide-range of fields and this piece gives the reader the knowledge to grasp these exciting developments.