Two-dimensional (2D) cadmium chalcogenide (CdX, X = Se, S, Te) colloidal nanoplatelets (NPLs) make up an emerging class of quantum well materials that exhibit many unique properties including uniform quantum confinement, narrow thickness distribution, large exciton binding energy, giant oscillator strength, long Auger lifetime, and high photoluminescence quantum yield. These properties have led to their great performances in optoelectrical applications such as lasing materials with a low threshold and large gain coefficient. Many of these properties are determined by the structure and dynamics of band-edge excitons in these 2D materials. Motivated by fundamental understanding of both 2D nanomaterials and their applications, the properties of 2D excitons have received intense recent interest. This Account provides an overview of three key properties of 2D excitons: how big is the 2D exciton (i.e., exciton center-of-mass coherent area); how the exciton moves in 2D NPLs (i.e., exciton in-plane transport mechanism); how multiple excitons interact with each other (i.e., biexciton Auger recombination); and their effects on the optical gain mechanism and threshold of colloidal NPLs. After a brief introduction in Section 1, the current understandings of 2D electronic structures of cadmium chalcogenide NPLs, and type-I CdSe/CdS and type-II CdSe/CdTe core/crown NPL heterostructures are summarized in Section 2. Section 3 discusses the direct measurement of exciton center-of-mass coherent area in 2D CdSe NPLs, its dependence on NPL parameters (thickness, lateral area, dielectric environment, and temperature), and the resulting giant oscillator strength transition (GOST) effect in 2D NPLs. 2D exciton diffusive in-plane transport in CdX NPLs and the comparison of exciton transport mechanisms in 2D NPLs and 1D nanorods are reviewed in Section 4. How Auger recombination lifetime depends on nanocrystal dimensions in NPLs, quantum dots, and nanorods is discussed in Section 5. The lateral area and thickness dependent Auger recombination rates of NPLs are shown to be well described by a model that accounts for the different dependence of the Auger recombination rates on the quantum confined and nonconfined dimensions. It is shown that Auger recombination rates do not follow the "universal volume scaling" law in 1D and 2D nanocrystals. Section 6 describes optical gain mechanisms in CdSe NPLs and the dependence of optical gain threshold on NPL lateral size, optical density, and temperature. The differences of optical gain properties in 0D-2D and the bulk materials are also discussed, highlighting the unique gain properties of 2D NPLs. At last, the Account ends with a summary and perspective of key remaining challenges in this field in Section 7.