  The rise of quantum information science has opened up a new venue for
applications of the geometric phase (GP), as well as triggered new insights
into its physical, mathematical, and conceptual nature. Here, we review this
development by focusing on three main themes: the use of GPs to perform robust
quantum computation, the development of GP concepts for mixed quantum states,
and the discovery of a new type of topological phases for entangled quantum
systems. We delineate the theoretical development as well as describe recent
experiments related to GPs in the context of quantum information.
