Generalized　finite　element　method　is　the　extension　of　conventional　finite　element　method.　Based　on　the　partition　of　unity　method,　it　improves　the　approximation　accuracy　of　the　finite　element　method　or　achieves　the　special　approximation　to　particular　problems　by　introducing　the　generalized　degrees　of　freedom　and　by　re-interpolating　the　nodal　degrees　of　freedom.　From　the　profound　study　on　constructing　the　shape　functions　of　the　generalized　finite　element　method,　arbitrarily　complex　problems　with　internal　features　(e.　g.　void,　inclusion　and　crack)　and　external　features　(e.　g.　re-entrant,　corner　and　edge)　can　be　expected　to　solve　by　the　simple　and　domain　independent　mesh.　The　essential　ideas　and　corresponding　strategies,　including　treatment　of　the　linear　dependency　and　boundary　conditions,　capture　of　the　local　approximation　functions,　numerical　integration　techniques,　are　introduced　in　details.　The　features　and　connections　are　analyzed　as　compared　with　the　extended　finite　element　method　and　the　finite　cover　method.　The　progress　of　the　generalized　finite　element　method　is　reviewed,　and　then　current　practical　applications　are　summarized.