Theoretical studies on the rotational and the vibrational transitions in molecular collisions are reviewed, with emphasis on the author's own work. Discussions in this article are mainly concerned with diatomic molecules. Part I begins with a brief historical introduction and a description of the scope of the present article. These are followed by introductory remarks on the relaxation times and the intermolecular interactions. In Part II, wave-mechanical formulation of the collision problem follows a brief description of the classical treatments. Then the rotational transitions in hydrogen molecules are discussed with the aid of the distorted wave method. Rotational transitions in other molecules present strong coupling problems, for which suggesting are made for approximate treatment. In Part III, the vibrational transitions in colinear collisions are discussed in detail. Then the present situation in the theory of three-dimensional collisions is summarized.