Tensor network renormalization group algorithms have, since the invention of the Multiscale Entanglement Renormalization Group and the Tensor Renormalization Group methods, proven to be useful tools in understanding emergent behavior in many-body systems, both numerically and conceptually. They provide efficient methods for numerically evaluating observables even for critical systems, and describe their emergent behavior in terms of renormalization group flows and information theoretic concepts such as entanglement structures. Like all tensor network methods, they can be equally well applied to systems of fermions and bosons, and to ones with strong couplings, since they are not based on Monte Carlo sampling, nor on perturbation theory. However, their major drawback is that so far they have been almost exclusively applied to (1+1)-dimensional quantum systems and 2-dimensional classical statistical mechanics systems, both of which can be described with 2-dimensional tensor networks. The objective of this research proposal is to improve the state of tensor network renormalization group methods, and most importantly, to transfer their success from 2D to 3D, where both the challenges and the rewards are far greater.