The time-average of a fluctuating flow often results in a nonzero mean. Suc
h steady streaming may result directly from the action of an oscillatory no
nconservative body force or, if such a force is conservative, indirectly th
rough the action of Reynolds stresses in the main body of the fluid or in t
hin boundary layers at no-slip boundaries. A theory for such streaming flow
s is developed for homogeneous fluids. For flows with a free surface it is
demonstrated that a mechanism for steady streaming exists even in an invisc
id fluid. Diverse areas in which steady streaming flows may be important ar
e discussed.