In the past, neutrinos played a fundamental role in the development of our understanding of the nuclear forces, when neutrinos served as probes to study the interior of hadrons. Today, neutrino-oscillation experiments can be viewed as natural interferometers sensitive to possible new physics. In particular, neutrinos can be used to test Lorentz invariance, a cornerstone of modern physics. In this talk, I will introduce a general formalism to study Lorentz violation and describe how we can search for possible deviations from exact Lorentz invariance using neutrino oscillations. I will also show how the breaking of Lorentz symmetry in neutrinos could explain some anomalous results that different experiments have observed in recent years. Additionally, I will describe the effects of Lorentz violation in tritium decay, polarized-neutron decay, and double beta decay and how we can use current and future experiments to search for the key signals of the violation of Lorentz invariance.