Mechanisms are now taken widely in philosophy of science to provide one of modern science’s basic explanatory devices. This has raised lively debate concerning the relationship between mechanisms, laws and explanation. This paper focuses on cases where a mechanism gives rise to a ceteris paribus law, addressing two inter-related questions: (1) What kind of explanation is involved? and (2) What is going on in the world when mechanism M affords behavior B described in a ceteris paribus law? We explore various answers offered by ‘new mechanists’ and others before setting out and explaining our own answers: (1) mechanistic explanations are a species of oldfashioned covering-law explanation and this often accounts in part for their explanatory p...