I will start by motivating the recent interest in non-relativistic gravity and strings, and introduce the basics of Newton-Cartan geometry. Newton-Cartan (NC) geometry was introduced more than 90 years ago in order to find a geometric formulation of Newtonian gravity. This geometry (including recent novel generalisation and extensions) has gained renewed interest as it appears in a variety of settings in modern theory involving gravity, string theory and holography. I will then talk about recent work on an action principle for non-relativistic gravity, including its Newtonian limit. This requires a new notion of NC geometry, which naturally arises in a covariant 1/c expansion of general relativity, with c being the speed of light. The corresponding non-relativistic truncation of general relativity goes beyond Newtonian gravity and is able to correctly describe gravitational time dilation. Finally, I will discuss the relevance and appearance of non-relativistic geometry in connection to non-relativistric string theory and holography.