Lattice Gauge theories are a central computational tool in numerically studying some of our most successful physical theories which arise in high energy and condensed matter physics. Yet standard approaches run into a variety of challenges, including the exponential growth of computational resources required as a function of system size (endemic to all of quantum mechanics), and the sign problem which arises when attempting to use probabilistic methods (generally Monte Carlo). In this talk, I will provide an overview of these (and other) challenges and discuss a particular tensor-network ansatz that can address them. Recent results for a system suffering from the sign problem will be presented.