Explore the foundations of synthetic Lorentzian geometry in this 51-minute talk by Michael Kunzinger, presented at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) as part of the Thematic Programme on "Geometry beyond Riemann: Curvature and Rigidity." Delve into the theory of Lorentzian (pre-)length spaces, focusing on the time separation function as the fundamental object. Discover how basic notions are derived from this function, including the definition of sectional curvature bounds through triangle comparison. Learn about the adaptation of methods from metric measure geometry and optimal transport to implement synthetic timelike Ricci curvature bounds. Gain insights into the application of these concepts in General Relativity, including recent developments in synthetic versions of Hawking's singularity theorem and vacuum Einstein equations.