Researching the philosophical aspects of explanation in the social sciences deserves special attention, because people form beliefs and make judgements about society everyday. This work tends to clarify the concept of explanation in this field by focusing on two important ways of explaining social science phenomena. In the first part of this work the first modern uses of explanation and understanding in the formative period of the development of the social sciences are explored, mainly through the 19th century. Hempel’s theory of explanation by subsumption under a covering law, which was the most popular way of explaining in the empirical sciences for a long time, is explicated, along with criticisms of the theory and of the notion of social law that is connected with it. The debate about social laws is exhibited, especially the usability of ceteris paribus laws. The possibility of exchanging the defective Hempel theory of explanation in the social sciences for an explanation based on social causal mechanisms is explored. Social mechanisms are also explored through the works of, in my opinion, some of the most relevant authors regarding this field from a sociological and philosophy of science point of view through an overview of the characteristics and latest research findings of this mode of explanation in the social sciences. Their connection with statistical social research and their causal aspect are also explored. This paper takes the position that for a successful explanation in the social sciences it is most useful to use a mechanisms based approach as a kind of upgrade of Hempel’s theory.