Colloidal monolayers are ideal systems for studying a wide range of phenomena, including ordering, dynamics, and phase behavior. In this thesis, we computationally investigate monolayers of two-dimensional (2D) circular colloids and quasi-two-dimensional (quasi-2D) ellipsoidal colloids to gain insight into the interplay between structure and dynamics and how it relates to the phase behavior.

In the case of isotropic circular colloids, we examine the collective motion in a crystal approaching the melting transition. To unambiguously identify rearrangement events in the crystal, we map molecular dynamics trajectories to a corresponding sequence of configurations of local potential energy minima ("inherent structures"). This process eliminates localized vibrational motion and results in a quantized energy spectrum. Within this spectrum, we identify distinct excited energy states characterized by highly cooperative large-scale motion facilitated by specific defect configurations, as well as a ground-state energy associated with small closed-loop motion without defect formation. In both cases, clusters of mobile particles can be separated into smaller groups of loop-like or string-like rearrangements. Ultimately, we find that the crossover between the average time the crystal spends in the ground state and the average time in the excited states can be used to predict crystal melting.

In the case of anisotropic ellipsoidal colloids, we systematically investigate the effect of out-of-plane confinement on phase behavior in quasi-2D systems. By investigating how confinement influences monolayer ordering, we provide a phase diagram across different concentrations and degrees of out-of-plane confinement. We identify the confinement at which quasi-2D systems begin to deviate from the 2D case, and characterize these changes in phase behavior. Finally, we observe a universal master curve that relates orientational order to rotational diffusion; we find a similar relationship between translational ordering and translational diffusion at moderate densities. Despite the differences in quasi-2D and strictly 2D monolayers, these relations provide a one-to-one mapping of quasi-2D systems onto strictly 2D systems with equivalent translational and rotational behavior.