In frustrated systems, competing interactions lead to degeneracies - which in turn produce complex phase diagrams and sometimes entirely new states
of matter. Frustration often arises from the lattice geometry, and a number of normally weak effects can be important to determining the state
of the system. I will discuss how coupling to phonons leads to a complex phase diagram for triangular lattice antiferromagnets and how quantum
fluctuations can stabilize a supersolid phase, where the system is at once both a crystal and a superfluid. Frustration can also arise from orbital
degrees of freedom, and I will discuss a promising candidate for a quantum liquid state with topological order, in a spin-orbital model.