Motivated by potential applications to holography and non-perturbative aspects of quantum field theory, the project will construct novel non-relativistic supergravity theories in 10, 11 and 3 dimensions. To do this, we will use recent insights into Newton-Cartan geometry, a differential geometry framework to describe non-relativistic space-times, and its connection to Riemannian geometry via state-of-the-art non-relativistic limit procedures. In 10 and 11 dimensions, we will focus on maximal non-relativistic supergravity theories that can be viewed as low energy descriptions of non-relativistic string and M-theory. We will use these to study dualities and properties of p-branes in non-relativistic string theory. We will furthermore propose and investigate a supersymmetric matrix model dual of non-relativistic M-theory. In 3 dimensions, we will construct matter coupled, off-shell, non-relativistic supergravity theories and use them to obtain non-relativistic supersymmetric field theories on curved backgrounds. In the relativistic case, the latter form a class of theories in which expectation values of particular observables can be computed exactly using supersymmetric localization. We will investigate whether similar results hold in the non-relativistic case, in particular in supersymmetric field theories on curved manifolds that are non-relativistic analogues of toy models that appeared in studies of graphene.