While there is no canonical notion of time in General Relativity, many spacetimes do admit time functions, which furthermore encode a lot of important information. In this talk, I will discuss the theory of time functions on Lorentzian length spaces, instead of Lorentzian manifolds. As will be seen during the talk, the most important classical results about existence and properties of time functions are still true in this more general setting. That includes the basic existence result for $K$-causal spaces, and the characterization of global hyperbolicity via Cauchy time functions. I will also point out some key differences, including the possibility of topology change.

This is joint work with A. Burtscher.