Trajectory approaches to quantum mechanics.- The Bohm hydrodynamic equations.- The phase space route to the hydrodynamic equations.- Quantum trajectories.- Fitting methods for computation of spatial derivatives.- Applications to wavepacket tunneling and decoherence.- Application to electronic transitions.- The initial value representation and correlation functions- Mixed quantum-classical dynamics.- Moving adaptive grids.- Trajectory approach to the density matrix.- Derivative propagation along quantum trajectories.- Quantum dynamics in phase space.- Non-Bohmain trajectory approaches to quantum mechanics.