The process of realizing the ground state of some typical (frustrated) quantum many-body systems, starting from the 'disordered' or excited states, can formally be mapped onto the search of solutions for computationally hard problems. The dynamics through quantum critical points are especially crucial in the context of such computational optimization problems and have been investigated intensively in recent times. Several successful methods are now well-established, and this volume compiles a collection of introductory reviews on such developments and related aspects. Written by well known experts, these lectures concentrate on quantum phase transitions and their dynamics as the transition or critical points are crossed. Both the quenching and annealing dynamics are extensively covered. The style has been kept as tutorial as possible in order to make this volume a suitable reference for young researchers joining this exciting and burgeoning field of research.