Summary: Philip Saffman made valuable theoretical contributions to different areas of low-Reynolds-number hydrodynamics. Three themes are selected for discussion here: (i) the lift force on a sphere in a shear flow at small, but finite Reynolds number, (ii) Brownian motion in thin liquid films, and (iii) particle motion in rapidly rotating flows. In addition, we give brief descriptions of some of Saffman’s other contributions including dispersion in porous media, the average velocity of sedimenting suspensions, and compressible low-Reynolds-number flows.