This talk provides a gentle introduction to some of the foundations of synthetic Lorentzian geometry. In the theory of Lorentzian (pre-)length spaces, the fundamental object is the time separation function (comparable to the metric in synthetic Riemannian geometry) and all basic notions are based on it. In particular, sectional curvature bounds can be defined via triangle comparison, and methods from metric measure geometry and optimal transport can be adapted to implement synthetic timelike Ricci curvature bounds. A main area of application is General Relativity, where synthetic versions of Hawking's singularity theorem and of the vacuum Einstein equations have recently been obtained.