The present disclosure relates to prosthetic valves configured to allow or encourage tissue adherence to polymeric surfaces of valvular structures thereof. In an example, a prosthetic valve can include a frame movable between a radially compressed state and a radially expanded state, and a valvular structure mounted inside the frame, the valvular structure comprising a plurality of leaflets. Each leaflet comprises a leaflet polymeric inner surface facing a central longitudinal axis of the prosthetic valve, and a leaflet polymeric outer surface facing the frame, wherein at least one of the polymeric surfaces of the leaflet comprises a tissue-adherent surface, configured to allow tissue adherence thereto.