  We present an expository account of the Bushell-Okrasi\'nski inequality, the
motivation behind it, its history, and several generalizations. This inequality
originally appeared in studies of nonlinear Volterra equations but very soon
gained interest of its own. The basic result has quickly been generalized and
extended in different directions strengthening the assertion, generalizing the
kernel and nonlinearity, providing the optimal prefactor, finding conditions
under which it becomes an equality, and formulating variations valid for other
than Lebesgue integrals. We review all of these aspects.
