The legs of animals, and their movements, have presumably been optimiz
ed by evolution and/or learning for the functions required of them in
life. This paper presents a series of studies in which attempts have b
een made to formulate optimization problems, to which the legs and the
ir movements may be solutions. These are studies of the ratio of radiu
s to wall thickness in tubular bones; of the strengths of bones; of te
ndon thickness; of the gaits of turtles and of mammals; and of the tec
hnique of human high jumping. They illustrate some serious difficultie
s that may arise in inverse optimization studies but also show that th
e approach is helping to improve our understanding of legs and gaits.