This paper discusses the prospect of the "new social history" guided by the recent work of Charles Tilly on the methodology of social and historical explanation. Tilly advocates explanation by mechanisms as the alternative to the covering law explanation. Tilly's proposals are considered to be the attempt to reshape the practices of social and historical explanation following the example set by the explanatory practices of molecular biology, neurobiology, and other recent "success stories" in the life sciences. Recent work in the philosophy of science on these practices by Peter Machamer, Lindley Darden, Carl Craver and others is used as the foil to disclose the difficulties of Tilly's project. Most important among them is the dilemma of specification: if diagrams (standard forms of the representation of mechanisms) are intended as representations of robust causal processes, they cannot be specific enough to provide complete mechanism schemata, and are bound to remain mechanism sketches. If mechanism sketches are elaborated in detail by tracing particular causal processes, they provide representations of fragile causal processes, which cannot be considered as mechanisms comparable to those in advanced life and other special sciences. Tilly's work on the explanation of mechanisms can be considered as symptomatic for the recent trend to visualize the forms of historical representation. As far as diagrams seem to be able to communicate stories in a direct way (without narrative discourse), this trend is a challenge for the theory of historical representation. The new theories of scientific explanation focusing on the explanatory practices of the life sciences can provide examples and be the source of inspiration for the work on the theory of historical and social explanation, going beyond the confines of the received framework of the covering law model of explanation.