This talk illustrates the complexities and pitfalls of hybrid systems verification. It describes a theoretical and practical foundation for deductive verification of hybrid systems called differential dynamic logic. The proof calculus for this logic is interesting from a theoretical perspective, because it is a complete axiomatization of hybrid systems relative to differential equations. The approach is of considerable practical interest too. Its implementation in the theorem prover KeYmaera has been used successfully to verify collision avoidance properties in the European Train Control System and air traffic control systems. The number of dimensions and nonlinearities in the hybrid dynamics of these systems is surprisingly tricky such that they are still out of scope for other verification tools.