The concept of nanotechnology is discussed, and its connection with biomedical engineering is elucidated. For the specific field of nanoscale flow and transport problems of physiological relevance, some typical examples are presented, and their interaction is discussed for some classic biomechanical problems like the flow in arteries with blood-wall coupling. Then, existing computational models are presented and classified according to the length scale of interest, with emphasis on particle-fluid problems. Final remarks address the essential unity of biomedical and engineering behaviour and the possible relevance to small-scale industrial research.