This review provides a current status report of the field concerning preparation of fibrous mats based on biodegradable (e. g., aliphatic polyesters such as polylactide or polycaprolactone) and conducting polymers (e. g., polyaniline, polypirrole or polythiophenes). These materials have potential biomedical applications (e. g., tissue engineering or drug delivery systems) and can be combined to get free-standing nanomembranes and nanofibers that retain the better properties of their corresponding individual components. Systems based on biodegradable and conducting polymers constitute nowadays one of the most promising solutions to develop advanced materials enable to cover aspects like local stimulation of desired tissue, time controlled drug release and stimulation of either the proliferation or differentiation of various cell types. The first sections of the review are focused on a general overview of conducting and biodegradable polymers most usually employed and the explanation of the most suitable techniques for preparing nanofibers and nanomembranes (i.e., electrospinning and spin coating). Following sections are organized according to the base conducting polymer (e. g., Sections 4-6 describe hybrid systems having aniline, pyrrole and thiophene units, respectively). Each one of these sections includes specific subsections dealing with applications in a nanofiber or nanomembrane form. Finally, miscellaneous systems and concluding remarks are given in the two last sections.