Semiconductor nanoplatelets (NPLs) are a type of two-dimensional (2D) nanomaterials with quantum confinement in the dimension of thickness. Similar to quantum confined quantum dots (QDs), photophysical properties of NPLs depends strongly on their thickness, but their large size in the unconfined lateral dimensions give rise to their other unique properties. The special 2D geometry also requires anisotropic synthesis in the colloidal solution. In this thesis, I study the photophysical properties and anisotropic growth by combing experiments with a powerful tool of kinetic Monte Carlo methods. Chapter 1 provides a review of the development of quantum confined nanocrystals on including discussions on their photophysical properties and anisotropic growth, gives a brief introduction to the kinetic Monte Carlo methods, and proposed some challenges in the field this thesis aims to address. In chapter 2, we propose a quantitative model of fluorescence quenching based on energy transfer mechanism of Fӧrster Resonance Energy Transfer (FRET) for binary mixtures of nanocrystals in colloidal solutions in the short-wavelength infrared (SWIR) region. This model is used to explain the fluorescence quenching of long-lifetime lead sulfide (PbS) quantum dots (QDs) mixed with plasmonic covellite copper sulfide (CuS) nanodisks (NDs), which serve as perfect fluorescent quenchers. By applying kinetic Monte Carlo methods which consider particle distributions and diffusion we are able to quantitatively reproduce experimental data which shows significant quenching at very small concentrations of NDs. The high concentration case is examined by conducting similar mixing experiments of mercury telluride (HgTe) NPLs and QDs, where we specifically discuss the impact of geometry on the distance dependence of energy transfer efficiency. Chapter 3 deals with a classic yet still puzzling phenomena in single-nanocrystal: photoluminescence intermittency (blinking). We apply Marcus theory of electron transfer to the blinking model of carrier trapping and detrapping, with meticulous mathematical analysis and kinetic Monte Carlo modeling. With canonical distribution of trap state energy, we quantitatively explain the difference between on and off time statistic in blinking cadmium telluride (CdTe) NPLs, as well as the temperature dependence of their quantum yield. In chapter 4, we focus on the anisotropic growth of NPLs, more specifically the different behaviors between cadmium selenide (CdSe) and cadmium telluride (CdTe) NPLs in terms of thickness selectivity and lateral size. We propose a simple kinetic model with 3 most important energetic parameters, on which kinetic Monte Carlo simulations of lattice are based. Using population percentage and evolution of size distribution from correlation function analysis, we offer a reasonable answer to questions regarding the difference of CdSe and CdTe NPLs. Finally, in chapter 5 we describe some of our ongoing effort towards further understanding of NPLs and QDs of interest, including using machine learning (ML) method to assist the optimization of synthetic conditions of NPLs and an in-depth study of correlation growth/ripening mechanisms with size distribution of QDs.