There are many kinds of interesting, insightful explanations in social science literature that lay claim to the honorific designation “scientific.” Weber explains, Durkheim explains, Marx explains, Keynes explains, Freud explains. Role theory explains, small-group theory explains, elite theory explains. The present paper integrates the various kinds of explanation found in social science through a problem-oriented account of social scientific methodology inspired by the philosophy of Sir Karl Popper. It also integrates explanation in the social sciences with explanation in the natural sciences. It is formulation and solution of problems that unifies science. All explanations are “efforts to deprive puzzles, mysteries, and blockages of their force, and hence, existence.” Scientific explanation, like explanation in general, removes the puzzling character of a phenomenon. A mechanism is found, the phenomenon is shown to be a specific case of a law-like generalization, or a flaws in initial conditions are discovered and corrected. A third kind of explanation, typically overlooked, is explanation by conceptual breakthrough. Breakthroughs remove the problematic character of a phenomenon by overcoming a blockage in thought. Problems or puzzles are often rooted in taken-for-granted or unconsciously-held assumptions. Scientific discovery may consist of such a wrenching away from taken-for-granted ways of thinking. Known facts or data are seen in a new way. It is thus the conceptual breakthrough, not new facts, mechanisms, or law-like generalizations that do the explaining. This article integrates a wide variety of kinds of explanation found in the social sciences by focusing on the various kinds of intellectual problems that arise in the social sciences, and the various types of explanation that solve these intellectual problems.