Studies of local adaptation provide important insights into the power of natural selection relative to gene flow and other evolutionary forces. They are a paradigm for testing evolutionary hypotheses about traits favoured by particular environmental factors. This paper is an attempt to summarize the conceptual framework for local adaptation studies. We first review theoretical work relevant for local adaptation. Then we discuss reciprocal transplant and common garden experiments designed to detect local adaptation in the pattern of deme x habitat interaction for fitness. Finally, we review research questions and approaches to studying the processes of local adaptation - divergent natural selection, dispersal and gene flow, and other processes affecting adaptive differentiation of local demes. We advocate multifaceted approaches to the study of local adaptation, and stress the need for experiments explicitly addressing hypotheses about the role of particular ecological and genetic factors that promote or hinder local adaptation. Experimental evolution of replicated populations in controlled spatially heterogeneous environments allow direct tests of such hypotheses, and thus would be a valuable way to complement research on natural populations.