The directionality and phase-dependence of the Josephson supercurrent provides a powerful probe of the phase anisotropy of unconventional superconductors and the nature of coherent states in hybrid devices incorporating superconductors and correlated materials. In this talk, I will review the technique of Josephson interferometry and describe how this approach has enabled us to determine the order parameter symmetry of unconventional superconductors. I will focus on two materials: the layered ruthenate superconductor Sr2RuO4, which is believed to have a complex px+ipy order parameter and exhibit chiral domains, and the heavy fermion superconductor UPt3, one of only a few superconductors known to exhibit two distinct superconducting phases. I will then describe ongoing Josephson interferometry experiments designed to nucleate and detect Majorana fermion states in topological insulators in proximity with superconductors.