The field of biological pumps is a subset of cardiac tissue engineering and focused on the development of tubular grafts that are designed generate intraluminal pressure. In the simplest embodiment, biological pumps are tubular grafts with contractile cardiomyocytes on the external surface. The rationale for biological pumps is a transition from planar 3D cardiac patches to functional biological pumps, on the way to complete bioartificial hearts. Biological pumps also have applications as a standalone device, for example, to support the Fontan circulation in pediatric patients. In recent years, there has been a lot of progress in the field of biological pumps, with innovative fabrication technologies. Examples include the use of cell sheet engineering, self-organized heart muscle, bioprinting and bio chambers for vascularization. Several materials have been tested for biological pumps and included resected aortic segments from rodents, type I collagen, and fibrin hydrogel, to name a few. Multiple bioreactors have been tested to condition biological pumps and replicate the complex environment during controlled culture. The purpose of this article is to provide an overview of the field of the biological pumps, outlining progress in the field over the past several years. In particular, different fabrication methods, biomaterial platforms for tubular grafts and examples of bioreactors will be presented. In addition, we present an overview of some of the challenges that need to be overcome for the field of biological pumps to move forward.