On the critical side it is argued that, contrary to a widespread view, the explanation of particular facts does not play a central role in pure science and hence that philosophers of science are misguided in supposing that the understanding of such explanations is one of the central tasks of the philosophy of science. It is suggested that the view being attacked may stem in part from an impression that the establishing of a general law is tantamount to the explanation of particular facts that “fall under” the law. This suggestion effects a bridge to the more positive part of the paper, which consists of an exploration of the complexities exhibited by the relation between the two activities. More specifically, I point out a number of disabilities, any one of which could prevent us from being able to explain particular facts that fall under a given law even after having established the law. Some of these have to do with the form of the law, and some have to do with our powers of detection vis-à-vis the particular facts in question. The former sort have to do with the ways in which laws may deviate from the strict-necessary-and-sufficient-condition ideal. The latter include the following points. (1) The individual explanatory factors may lie beyond our present powers of detection. (2) The complexity of such factors may be too great for us to be able to interrelate them. (3) We may be unable to apply concepts used in the law to facts in this area (although they are in fact applicable).