Biomedical catheters are thin hollow tubes inserted into the human body to accurately measure various physiological parameters during invasive surgical procedures and diagnostic methods. Sensors realized using micro-/nano-electro-mechanical systems (MEMS/NEMS) technology are integrated with catheters to measure blood pressures, flows, pH- and glucose levels, and temperature. Of these physiological parameters, pressure sensing is of significant importance in identifying and treating various biomedical conditions. Piezoresistive technique is a widely investigated and preferred sensing mechanism to realize miniature sensors for its numerous advantages. In this paper, we critically review biomedical catheters as well as miniature piezoresistive pressure sensors developed for catheters. First, the evolution of catheters and their applications in measuring physiological parameters are discussed in detail. Next, the progress of piezoresistive pressure sensors developed for integration with catheters are described under three broad categories by considering various aspects such as diaphragm shape, material & size, piezoresistor type & material, readout type, fabrication processes, salient features of the device, and packaging techniques. A detailed section is devoted to alternative recent piezoresistive materials, including silicon nanowire (SNW), carbon nanotube (CNT), and Graphene. Finally, the process of catheterization and testing of biomedical catheters with integrated pressure sensors in the clinical environment are elaborated.