Many legal cases require decisions about causality, responsibility or blame, and these may be based on statistical data. However, causal inferences from such data are beset by subtle conceptual and practical difficulties, and in general it is, at best, possible to identify the "probability of causation" as lying between certain empirically informed limits. These limits can be refined and improved if we can obtain additional information, from statistical or scientific data, relating to the internal workings of the causal processes. In this paper we review and extend recent work in this area, where additional information may be available on covariate and/or mediating variables.