Flagellated bacteria swim by rotating long, thin, helical filaments that arise at different points on the cell surface.  Each filament is driven at its base by a rotary motor only 45 nm in diameter made from about 20 different kinds of parts.  Control of the direction of rotation of such motors is the basis for the chemotactic response, i.e., for the ability of cells to swim up spatialgradients of chemical attractants.  I will review the history of this subject, tell you about the motion of E. coli, and outline the signal transduction pathway that links chemoreceptors to flagella.  I will describe some of the methods (fluorescence, FRET, BRET) that we have used to probe this remarkable molecular system.