We study field theories and gravitational models based on non-Lorentzian spacetime structures, such as Galilean, Carrollian, Aristotelian, and Lifshitz geometries. We use these frameworks to investigate non-AdS extensions of gauge/gravity dualities, including non-relativistic holography and the Carrollian perspective on flat space holography. At the same time, we apply non-Lorentzian methods to construct effective field theories for quantum matter systems, such as the fractional quantum Hall effect, fractons, and flat band systems, some of which admit a bulk/boundary description.