Quantum Phenomena are ubiquitous in complex molecular systems - as revealed by findings from experimental observations based upon ultrafast spectroscopic techniques - and yet remain a challenge for theoretical analysis. The present volume examines and reviews the state-of-the-art in matching theoretical concepts and methods with the observed phenomena. Emphasis is on complex molecular processes involving surfaces, clusters and solute-solvents in various materials and biological systems using quantum dynamical, trajectory-based and statistical methods for the description of these processes.