Photon emission correlation spectroscopy (PECS) is an indispensable tool for the study of atoms, molecules, and, more recently, solid-state quantum defects. In solid-state systems, its most common use is as an indicator of single-photon emission, a key property for quantum technology. Beyond single-photon purity, photon correlation measurements can provide a wealth of information that can reveal details about an emitter's electronic structure and optical dynamics that are hidden by other spectroscopy techniques. This thesis explores the application of PECS to study and understand the optical dynamics of quantum emitters. The first part of this thesis presents a guide to a standardized framework for using PECS to facilitate materials exploration for qubit candidates. This includes discussion of theoretical background, considerations for data acquisition and statistical analysis, and interpretation of PECS. It also illustrates how this experimental technique can be paired with optical dynamics simulations to formulate an electronic model for unknown quantum emitters. The second part of this thesis implements the practices discussed in the first part to explore the optical dynamics of two systems: the nitrogen-vacancy (NV) center in diamond and a quantum emitter in hexagonal boron nitride (h-BN). The NV center is a promising platform for applications in quantum sensing, quantum communication, and quantum networks. In particular, its spin and charge dynamics constitute useful attributes that can be harnessed for quantum control protocols. This thesis models and quantifies the transition rates that govern spin and charge dynamics in the NV center, utilizing PECS measurements, analysis, and simulations as a function of magnetic field, and excitation power. These findings can further inform the design of quantum control protocols. H-BN hosts pure single-photon emitters that have shown evidence of optically detected electronic spin dynamics. However, the electrical and chemical structure of these optically addressable spins is unknown, and the nature of their spin-optical interactions remains mysterious. This thesis discusses time-domain optical and microwave experiments to characterize a single emitter in h-BN exhibiting room temperature optically detected magnetic resonance. It further discusses use of dynamical simulations to constrain and quantify transition rates in the model, and design of optical control protocols that optimize the signal-to-noise ratio for spin readout. This constitutes a necessary step towards quantum control of spin states in h-BN.