Cytoskeletal motor proteins move on filamentous tracks by converting input chemical energy that they derive by catalyzing the hydrolysis of ATP. The ATPase site is the analogue of an engine and hydrolysis of ATP is the analogue of burning of chemical fuel. Moreover, the functional role of a segment of the motor is analogous to that of the transmission system of an automobile, which consists of a shaft, gear, clutch, etc. The operation of the engine is intrinsically ‘noisy’ and the motor faces a molecular ‘hailstorm’ in the aqueous medium. In this commemorative review, we celebrate the centenary of Michaelis and Menten's landmark paper of 1913 and the golden jubilee of Monod and colleagues classic paper of 1963 by highlighting their relevance with respect to explaining the operational mechanisms of the engine and the transmission system, respectively, of cytoskeletal motors.