Obtaining an accurate microscopic description of water structure and dynamics is of great interest to molecular biology researchers and in the physics and quantum chemistry simulation communities. This dissertation describes efforts to apply quantum Monte Carlo methods to this problem with the goal of making progress toward a fully "ab initio" quantum mechanical description of water that is accurate, efficient, and free of uncontrolled approximations. The projects described in this work are largely concerned with addressing three major challenges, described here. We use Path Integral Monte Carlo to study proton zero point motion. We report on several technical aspects of implementing path integrals in Monte Carlo simulations of water: careful studies of convergence with respect to the number of discrete imaginary time slices; if pair product actions can improve convergence over the primitive approximation; handling the non-trivial geometry of the water molecule, including numerical evaluation of the exact density matrix for rotations of a rigid asymmetric rotor. Questions remain about the ability of self consistent DFT-GGA calculations to accurately describe the electronic structure of water. Because Diffusion Monte Carlo (and other projector methods) accept wave functions that explicitly include correlations and improve on a trial wave function by projecting the overlap with the exact ground state, we are motivated to ask if QMC results are more accurate than DFT. We present a set of benchmark data from Diffusion Monte Carlo calculations on configurations of 32 water molecules at various temperatures, believed to be the first systematic investigation of bulk water using DMC. Finally, and most generally, autocorrelation times for energies and structural properties are very long, on the order of thousands of Monte Carlo cycles or picoseconds of Molecular Dynamics integration. Thus a great deal of computational effort is required to generate statistically independent, well-converged data. This problem affects all water simulations, but the implications are most severe for "ab initio" methods, where the cost for a single simulation step is very high to begin with. We describe a number of approaches to address this challenge and their utility and outlook. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]