Abstract: We review both the kinematics and dynamics of non-lorentzian theories. First, we introduce non-lorentzian kinematical spacetimes and their symmetry algebras.  Next, we construct actions describing the particle dynamics in some of these kinematical spaces using the method of nonlinear realisations.  We continue discussing  three types of non-lorentzian gravity theories: Galilei gravity, Newton-Cartan gravity and Carroll gravity.