A path geometry on a manifold is a collection of
unparameterized curves with the property that through any point, there
is exactly one curve passing through this point in each tangent
direction. A flat model is given by the set of lines in Euclidean
space. More generally, one can consider geodesics of a metric.
Locally, path geometries are described by second-order systems of
ordinary differential equations. In this talk, I will begin with a
review of the general theory of path geometries, in particular
describing the notions of torsion and curvature. I will then show how
such structures naturally arise in many geometric contexts, enabling
the study of various geometric structures in a unified way. I will
focus on (para)CR-geometry.