Analytical sociology focuses on social interactions among individuals and the hard-to-predict aggregate outcomes they bring about. It seeks to identify generalizable mechanisms giving rise to emergent properties of social systems which, in turn, feed back on individual decision-making. This research program benefits from computational tools such as agent-based simulations, machine learning, and large-scale web experiments, and has considerable overlap with the nascent field of computational social science. By providing relevant analytical tools to rigorously address sociology’s core questions, computational social science has the potential to advance sociology in a similar way that the introduction of econometrics advanced economics during the last half century. Computational social scientists from computer science and physics often see as their main task to establish empirical regularities which they view as “social laws.” From the perspective of the social sciences, references to social laws appear unfounded and misplaced, however, and in this article we outline how analytical sociology, with its theory-grounded approach to computational social science, can help to move the field forward from mere descriptions and predictions to the explanation of social phenomena.