Carbon nanomembranes (CNMs) are synthetic 2D carbon sheets with tailored physical or chemical properties. These depend on the structure, molecular composition, and surroundings on either side. Due to their molecular thickness, they can be regarded as "interfaces without bulk" separating regions of different gaseous, liquid, or solid components and controlling the materials exchange between them. Here, a universal scheme for the fabrication of 1 nm-thick, mechanically stable, functional CNMs is presented. CNMs can be further modified, for example perforated by ion bombardment or chemically functionalized by the binding of other molecules onto the surfaces. The underlying physical and chemical mechanisms are described, and examples are presented for the engineering of complex surface architectures, e.g., nanopatterns of proteins, fluorescent dyes, or polymer brushes. A simple transfer procedure allows CNMs to be placed on various support structures, which makes them available for diverse applications: supports for electron and X-ray microscopy, nanolithography, nanosieves, Janus nanomembranes, polymer carpets, complex layered structures, functionalization of graphene, novel nanoelectronic and nanomechanical devices. To close, the potential of CNMs in filtration and sensorics is discussed. Based on tests for the separation of gas molecules, it is argued that ballistic membranes may play a prominent role in future efforts of materials separation.