Glasses are physical systems that lack structural order and exhibit extremely slow dynamics, which makes them challenging to study. In this thesis we apply Monte Carlo methods to two distinct glassy systems: the 3D Edwards-Anderson spin glass and a binary hard sphere fluid. While significant progress has been made on theoretical and experimental fronts, much of our current understanding of glasses has come from numerical simulations. Standard Monte Carlo techniques cannot be used to perform equilibrium simulations due to slow dynamics in the glassy regime. As a result, several specialized techniques have been developed in order to simulate such systems, including the main topic of this thesis, population annealing Monte Carlo. Population annealing is a sequential Monte Carlo algorithm used to perform equilibrium simulations of systems with rough free energy landscapes, such as glasses. Unlike standard Monte Carlo algorithms, which are unable to overcome large free energy barriers, population annealing is able to sample disparate regions of configuration space in parallel. In this thesis, we discuss the optimization, analysis, and application of population annealing to model glassy systems. The 3D Edwards-Anderson spin glass has a long history of research, however, the nature of its low-temperature phase remains unclear. We use a carefully optimized canonical ensemble version of population annealing in order to obtain new benchmark values of observables that are important to understanding its low-temperature phase. We also derive and numerically test several useful metrics that provide accurate estimates of the systematic and statistical errors of a simulation. The binary hard sphere fluid is an example of a system that undergoes a dynamic transition from a fluid to a disordered glassy solid. Whether this system also undergoes a thermodynamic glass transition remains an open question. We use an NVT ensemble version of population annealing in order to simulate the binary fluid at high density and we present two new methods to measure the configurational entropy deep in the glass regime. Using our new numerical techniques, we are able to predict the location and existence of the thermodynamic glass transition.