Abstract: I will start by outlining some basic ideas of the geometric theory of differential equations. Then I will discuss the classical concept of path geometries as a geometrization of 2nd order ODE's and relate it to a certain parabolic geometry. Finally, I will show how general tools from the theory of parabolic geometries lead to effective invariants for such equations. These invariants can be used to recognize trivial equations and geodesic equations among general 2nd order ODE's and for generic equations in a certain class even lead to explicit solutions.