This book is devoted to the presentation and discussion of some models of relevance in Celestial Mechanics and Astrodynamics. The motions of celestial bodies, either natural or artificial, are governed by conservative forces, like the gravitational attraction that preserve the total energy and by dissipative forces, like the tidal torque, Stokes drag, and the Poynting-Robertson effect. The basic idea of this book is to describe in each chapter a model in the conservative setting, providing its main features, and then to extend the model by including dissipative forces.