In recent years, there has been rapid growth in the research field of real-time observation of nuclear and electronic dynamics in molecules. Its time range extends from femtoseconds to attoseconds. This has been made possible by the development of both laser technology and time-dependent theoretical treatments. Indeed, this research field is arguably the most active one in molecular science, second only to femtosecond chemistry. The outcome of the research is expected to make an important contribution to physics, materials science and biology as well as chemistry.In this monograph, the fundamental theories and methods, as well as experimental methods and results, of real-time observation of both nuclear and electronic motions in molecular systems are described. It is suitable for researchers who want to make an active contribution to the new research field and for graduate students who are interested in ultra-fast nuclear and electron dynamics in molecular systems.