A conveying device at least for conveying a conveying medium includes at least one conveying space, with at least one conveying space element, which at least partly delimits the conveying space and is embodied in a rigid fashion, and with at least one elastically deformable conveying element which delimits the conveying space together with the conveying space element. The conveying space element includes at least one concave recess for at least partly forming the conveying space, wherein an inner surface of the conveying space element, which delimits the concave recess, forms a wall of the conveying space, wherein the conveying element comprises at least one conveying surface, which is utilizable in targeted fashion for a conveyance of a fluid in the conveying space and/or through the conveying space.