The physics of the solid state offers an amazing variety of quantum phenomena. Amongst the most exotic is superconductivity - the ability of material to conduct electricity without resistance. I am currently interested in the physics of so-called "unconventional" superconductors, which have properties that cannot be explained by the Nobel-prize-winning 1955 theory of Bardeen, Cooper, and Schrieffer. I am particularly interested in the interplay of superconductivity with spin-orbit coupling, which is a ubiquitous feature of solid state systems. In some cases, this coupling is so strong that it can force the electrons to behave as if they are in fact spin-3/2 particles. Together with my collaborators, I have already identified a number of systems where this could lead to highly unusual superconducting states.