  General conditions for the occurrence of mesoscopic phase fluctuations in
condensed matter are considered. The description of different thermodynamic
phases, which coexist as a mixture of mesoscopically separated regions, is
based on the {\it theory of heterophase fluctuations}. The spaces of states,
typical of the related phases, are characterized by {\it weighted Hilbert
spaces}. Several models illustrate the main features of heterophase condensed
matter.
