We review Wright's original definitions of the genetic correlation coefficients F(ST), F(IT), and F(IS), pointing out ambiguities and the difficulties that these have generated. We also briefly survey some subsequent approaches to defining and estimating the coefficients. We then propose a general framework in which the coefficients are defined, their properties established, and likelihood-based inference implemented. Likelihood methods of inference are proposed both for bi-allelic and multi-allelic loci, within a hierarchical model which allows sharing of information both across subpopulations and across loci, but without assuming constancy in either case. This framework can be used, for example, to detect environment-related diversifying selection.