Lately there has been renewed interest in two-dimensional gauge theories, stemming from their applicability as toy models of QCD along with rapidly advancing techniques for simulating them both numerically and experimentally. I will start by discussing the U(1) theory coupled to a fermion in two dimensions, and important lessons from its ABJ anomaly that can be used to dramatically improve the accuracy of results obtained from the Hamiltonian lattice. These methods enable very precise calculations outside of the perturbatively accessible regime. I will then discuss recent progress on non-abelian theories coupled to an adjoint Majorana fermion. In this case, all the mixed 't Hooft anomalies are naturally realized in a Hamiltonian lattice formulation, and we obtain numerical results that go beyond the capabilities of other methods.

(Online Talk)