The study of the low energy collective and single particle excitations of medium and heavy nuclei has undergone a rapid development in recent years. The aim of this text is to survey and assess this development, from both the experimental and theoretical perspectives, using an approach that emphasizes simple physical and intuitive pictures as an aid to understanding the empirical systematics as well as detailed model calculations. The approach is simple and intuitive and is well suited to the needs of graduate students in this area.