Colloidal metal-halide perovskite nanocrystals (MHP NCs) are gaining significant attention for a wide range of optoelectronics applications owing to their exciting properties, such as defect tolerance, near-unity photoluminescence quantum yield, and tunable emission across the entire visible wavelength range. Although the optical properties of MHP NCs are easily tunable through their halide composition, they suffer from light-induced halide phase segregation that limits their use in devices. However, MHPs can be synthesized in the form of colloidal nanoplatelets (NPls) with monolayer (ML)-level thickness control, exhibiting strong quantum confinement effects, and thus enabling tunable emission across the entire visible wavelength range by controlling the thickness of bromide or iodide-based lead-halide perovskite NPls. In addition, the NPls exhibit narrow emission peaks, have high exciton binding energies, and a higher fraction of radiative recombination compared to their bulk counterparts, making them ideal candidates for applications in light-emitting diodes (LEDs). This review discusses the state-of-the-art in colloidal MHP NPls: synthetic routes, thickness-controlled synthesis of both organic-inorganic hybrid and all-inorganic MHP NPls, their linear and nonlinear optical properties (including charge-carrier dynamics), and their performance in LEDs. Furthermore, the challenges associated with their thickness-controlled synthesis, environmental and thermal stability, and their application in making efficient LEDs are discussed.