  We study Li-Yorke chaos and distributional chaos for operators on Banach
spaces. More precisely, we characterize Li-Yorke chaos in terms of the
existence of irregular vectors. Sufficient "computable" criteria for
distributional and Li-Yorke chaos are given, together with the existence of
dense scrambled sets under some additional conditions. We also obtain certain
spectral properties. Finally, we show that every infinite dimensional separable
Banach space admits a distributionally chaotic operator which is also
hypercyclic.
