The underlying basis of how swimming organisms propel themselves forward against resistance from the surrounding fluid has been studied for almost a century. Many traditional analyses have centered on decomposing the total force on a swimming body into drag and thrust. The validity of this decomposition has been controversial since it is not expected to hold for finite Reynolds number swimming. Yet, we report an approximate drag-thrust decomposition for one class of undulatory propulsors - the ribbon fins of gymnotiform and balistiform swimmers. The conclusion is based on high-resolution numerical simulations to calculate the force acting on an undulatory ribbon fin of the black ghost knifefish (Apteronotus albifrons). We show that drag-thrust decomposition is possible because there is very little spatial overlap between the drag-associated flow field and the thrust-associated flow field. This decomposition is different from the decomposition due to Lighthill that has been widely discussed in literature over the past four decades. The results above are used to interrogate balistiform and gymnotiform swimmers that move by undulating elongated ribbon fins attached to a body that is held nearly rigid. The question of whether this evolutionary adaptation may have a hydrodynamic basis was considered by Lighthill and Blake. They proposed, based on Lighthill's elongated body theory, that the ability of the ribbon fin to generate thrust is enhanced by the presence of a rigid body. This mechanism, commonly referred to as “momentum enhancement”, has been widely discussed in literature over the past two decades. Our results show that there is no momentum enhancement. This is explained by noting that the dominant mechanism of thrust generation by ribbon fins is different from that assumed in the theoretical approach of Lighthill. Nevertheless, many features of the morphology of gymnotiform and balistiform swimmers do appear to have a hydrodynamic basis. Specifically, it is found that the observed height of the ribbon fin, for a given body size, is such that the mechanical energy spent per unit distance, i.e., the mechanical cost of transport (COT) is optimized. Many open issues remain. First, it remains to be explored whether the drag-thrust decomposition can be extended to anguilliform and carangiform swimming. Second, while we have found optimal fin height for gymnotiform and balistiform swimmers for a given body size, it is still unclear whether keeping part of the body rigid is hydrodynamically better compared to a mode of swimming where the entire body is undulated (like in anguilliform swimming). Preliminary results interrogating these aspects will be discussed.