This practical book presents an overview of the various approaches developed to understand the dynamics of electronic systems in physics and chemistry. It also illustrates typical application examples, namely atoms, molecules, and clusters such as nano objects. For each system, the book reviews its key features and concepts and also provides a wider perspective on other physical systems such as atomic nuclei and quantum dots. There exist a large number of theories adapted to specific physical situations (both in space and time), but there is not yet a common theory for all possible dynamical scenarios. This book provides a general perspective on the topic, supplying the reader with a guidebook to navigate the wide spectrum of approaches. It provides an overview of available theories to address various problems in the irradiation of finite systems, discussing the possibilities and limitations of the available theories to help readers understand the applicability of a given theory or set of theories to address a given physical problem or chemical situation. It is an ideal guide for graduate students and researchers in physics and chemistry. Key Features: - Presents a critical survey of available theoretical tools to help readers choose the appropriate method or approach for any given physical situations - Accessible, with an emphasis on avoiding details of formal and technical difficulties - Provides a guided tour based on typical examples starting from the actual physical situation down to actual tools to be used to describe it Jorge José Kohanoff is a Professor of Computational Chemical Physics at Queen's University Belfast, Ireland. Paul-Gerhard Reinhard is a Professor at the Institute for Theoretical Physics at the University of Erlangen-Nuremberg, Germany. Lorenzo Stella is Senior Lecturer in the Centre for Laser-Matter Interactions (CLMI) at the Queen's University Belfast, United Kingdom. Eric Suraud is a Distinguished Professor at Paul Sabatier University, France.