III-V colloidal nanocrystals, such as InP, have emerged as a viable alternative to their heavily optimized II-VI counterparts, owing to their lower toxicity and enhanced structural stability. However, the III-V bonds are predominantly covalent, making it difficult to achieve microscopic reversibility for defect-free crystal growth, except at elevated temperatures inaccessible to traditional organic solvents. Additionally, the confinement sizing curve dictates that blue emission would only be achievable from minuscule InP nanocrystals that are inherently unstable. We address these challenges by introducing molten halide salts as reaction media for performing In-to-Ga cation exchange to synthesize alloyed In1-xGaxP nanocrystals with a bandgap greater than their InP counterparts. Subsequent sections in this dissertation present a comprehensive study of emissive In1-xGaxP nanocrystals, including the kinetic factors governing In-to-Ga cation exchange, variations in excitonic oscillator strength in relation to gallium composition, and synthetic strategies to achieve stable blue emission.In Chapter 2, we estimate the kinetic factors that govern isovalent In-to-Ga cation exchange in InP nanocrystals. The gallium halide molten salt reaction medium causes surface recrystallization of spherical InP nanocrystals to yield tetrahedral In1−xGaxP nanocrystals during high-temperature annealing. We estimate the activation energy of Ga exchange in nanocrystalline InP at ~0.9 eV, considerably lower than the activation energy measured for self-diffusion in the corresponding bulk systems. It has long been debated if crystal momentum k is a useful quantum number to describe band structure in quantum-confined nanocrystalline systems, which blur the distinction between direct and indirect gap semiconductors. Bulk crystals of In1-xGaxP constitute a prototypical platform for analyzing band structure in ternary III-V alloys of direct- and relatively narrow-gap InP with indirect- and relatively wide-gap GaP. The direct-to-indirect band gap transition in nanocrystalline In1-xGaxP is investigated in Chapter 3 by producing an optimized synthetic protocol for In-to-Ga cation exchange in inorganic molten salts, and subsequently growing ZnS shells on In1-xGaxP to form bright core-shell In1-xGaxP/ZnS QDs. Time-resolved PL studies indicate that the oscillator strength of excitonic transitions decreases with gallium incorporation, represented by a monotonic increase in radiative decay lifetime. The direct-to-indirect gap transition occurs with roughly the same composition dependence as in bulk In1-xGaxP, demonstrated by the loss of an excitonic bleach feature in transient absorption. Therefore, we must strike a balance between the nanocrystal size and gallium composition to achieve blue emission from alloyed In1-xGaxP nanocrystals while preserving the oscillator strength of direct-like interband transitions. In Chapter 4 we outline a protocol to prepare In1-xGaxP quantum dots by performing In-to-Ga cation exchange on small InP nanocrystals to achieve one of the first instances of bright and color pure blue emission from III-V nanocrystals. Compared to InP, In1-xGaxP has a better lattice constant match with ZnS, allowing us to overgrow a relatively thick ZnS shell. We demonstrate that the resulting commensurability of the core and shell leads to increased thermal stability of their PLQY. Our co-optimization of size and composition in the In1-xGaxP system establishes cation exchange in molten salts as a viable route to high-quality, nontoxic III-V QD emitters for display applications.