This review paper focuses on forensic aspects of the relation between statistics and genetics. Some of the scientific achievements of the Swedish psychiatrist and geneticist Erik Essen-Möller may be viewed in the above interdisciplinary context. In a number of situations the correct familial relation between a group of individuals is required. We discuss recent work done to relax some assumptions involved in the classical calculations in Essen-Möller (1938). Moreover, we extend the discussion to identification problems. In a given case there may be a large number of possible family constellations or pedigrees. A prior probability distribution is established. The posterior model accounts for the combinatorial complexities of the pedigrees, mutations, kinship, and uncertainty in allele frequencies. Examples are based on the shareware program FAMILIAS, see http://www.nr.no/familias. A main message of the present paper is that the Bayesian approach is a convenient framework to down-weight unreasonable (e.g. incestuous) pedigrees that may always appear likely if only DNA-measurements are used.