The fact that neutrinos have mass allows them to possess many other properties, like a magnetic dipole moment and a finite decay width. Theoretical expectations for these are, however, well beyond current experimental bounds, and the discovery of new exotic neutrino properties would indicate the presence of (more) new physics. Here, I review some of the current bounds on exotic neutrino properties. Neutrino experiments are unique probes of several fundamental space-time symmetries, including invariance under CP and Lorentz transformations. I discuss how precision neutrino experiments are used to test some of the most fundamental principles of physics at unprecedented levels.