  We study an analogue of fibrations of topological spaces with the homotopy
lifting property in the setting of C*-algebra bundles. We then derive an
analogue of the Leray-Serre spectral sequence to compute the K-theory of the
fibration in terms of the cohomology of the base and the K-theory of the
fibres. We present many examples which show that fibrations with noncommutative
fibres appear in abundance in nature.
