In the last two decades remarkable progress has been made in understanding and describing tunneling processes in complex systems in terms of classical trajectories. This book introduces recent concepts and achievements with particular emphasis on a dynamical formulation and relations to specific systems in mesoscopic, molecular, atomic and nuclear physics. Advanced imaginary time techniques, e.g. for decay rates and tunnel splittings, are discussed in the first part. The second part covers current developments for wave-packet tunneling in real-time, and the third part describes thermodynamical and nonequilibrium approaches for barrier transmission in dissipative systems.