Understanding and predicting the properties of quantum many-particle systems remain a theoretical and computational challenge. In materials simulations, the standard model is an independent-electron approach in the framework of density-functional theory. In systems where the effects of particle interaction are strong, this approach is often inadequate. Several alternatives are being pursued. Among these, we have been developing a non-perturbative Monte Carlo approach using auxiliary fields. Our approach takes the form of a linear superposition of independent-particle calculations in fluctuating external fields. The different field configurations are "entangled" by random walks. An approximate solution is formulated to control the sign problem. I will discuss progress and prospects in the development and application of this approach. Results will be presented on lattice models for ultracold atomic gases, and on electronic structure computations in molecular systems and bulk materials.