Semiconductor nanocrystals, also known as quantum dots (QDs), are an important class of materials that are being extensively studied for a wide variety of potential applications, such as medical diagnostics, photovoltaics, and solid-state lighting. The optical and electronic properties of these nanocrystals are different from their bulk properties and depend on the size of the QDs. Therefore an important requirement in their synthesis is a proper control on the final nanoparticle size. Recently, a technique has been developed for synthesizing zinc selenide (ZnSe) QDs using microemulsion droplets as templates. In these systems, a fixed amount of a reactant is dissolved in each droplet and a second reactant is supplied by diffusion through the interface. Spontaneous reaction between the two reactants at the droplet interface forms ZnSe nuclei, whose subsequent diffusion and coalescence into clusters ultimately leads to the formation of a single particle in each droplet. The size of the final particle can be adjusted by changing the initial concentration of the reactant that is dissolved in the dispersed phase of the microemulsion. In this thesis we use a modeling and simulation approach to study the phenomena underlying the formation of QDs in the droplets of a microemulsion. A Lattice Monte-Carlo model was developed to describe Brownian diffusion of a Zn-containing precursor (reactant) inside a droplet, formation of ZnSe nuclei via an irreversible reaction with a Se-containing precursor at the droplet interface, Brownian diffusion and coalescence of nuclei into clusters ultimately leading to the formation of a single nanoparticle inside the droplet. The time required for forming a single particle was found to initially increase as the final particle size was increased by increasing the initial concentration of the reactant in the droplet, but it quickly passed through a maximum, and subsequently decreased. The simulations revealed that this seemingly anomalous result can be explained by studying the intermediate cluster populations that show the formation of a large intermediate "sweeper" cluster. This sweeper cluster is a more effective collision partner to smaller ones and accelerates the coalescence process that eventually leads to the formation of a single particle. A generalized dimensionless equation was obtained that relates the formation time of the final particle to its size for various droplet sizes and diffusivities of the reactant and clusters in the droplet. A parametric study revealed that the final particle formation time is more sensitive to changes in the cluster coalescence probability than in the probability of nucleation. We subsequently compared these results with those obtained by simulating the coalescence of nuclei that are assumed to be formed spontaneously inside a droplet and to be initially uniformly dispersed in it. Comparison of the time required for forming a single final particle for the two cases revealed that for ZnSe particles with diameter smaller than 3.5 nm the predicted formation times were approximately the same. Surprisingly, for particles larger than 3.5 nm, the scenario that required diffusion of a reactant to the interface and formation of nuclei via a reaction at the interface led to the formation of a single particle faster than the scenario that started with nuclei uniformly dispersed in the droplet. Analysis of intermediate cluster populations indicates that the "sweeper" clusters are more effective in accelerating cluster coalescence when the nuclei are supplied gradually, as in the first scenario, compared to spontaneous nucleation throughout the domain. Generalized equations were obtained that describe the evolution of the number of different cluster sizes during coalescence starting from an initially monodispersed population of nuclei thus extending the classical theory of coalescence of monodisperse aerosols in an infinite domain to include coalescence in finite spherical domains with reflective boundaries. Finally, a generalized phenomenological model describing an energy balance during coalescence of two nanoparticles was developed. The reduction in the surface area of the coalescing system was modeled to be the source of thermal energy released due to the formation of additional bonds in the bulk of the coalesced particles. The temperature rise of the coalescing system was predicted for adiabatic coalescence and for coalescence with energy dissipation to a surrounding medium. Generalized equations were developed by scaling the temperature rise with its maximum value that corresponds to adiabatic conditions and the time with a characteristic time for coalescence obtained from the literature that depends on the mechanism (e.g., viscous flow, bulk diffusion, or surface diffusion). As a case study, the effects of the size of coalescing ZnSe nanoparticles on the temperature evolution of the coalescing system were studied by assuming that surface diffusion is the predominant mechanism for coalescence in this system. This modeling and simulation study of nanoparticle nucleation and coalescence presented in this thesis has revealed new phenomena and led to generalized models that can be used for studying such systems. Our work extended the classical theory for coalescence in an infinite domain to include finite spherical domains with reflective boundaries and provided a generalized approach for the analysis of transient thermal effects occurring during coalescence of two nanoparticles.