  We give a summary of the status of current research in stochastic
semiclassical gravity and suggest directions for further investigations. This
theory generalizes the semiclassical Einstein equation to an Einstein-Langevin
equation with a stochastic source term arising from the fluctuations of the
energy-momentum tensor of quantum fields. We mention recent efforts in applying
this theory to the study of black hole fluctuations and backreaction problems,
linear response of hot flat space, and structure formation in inflationary
cosmology. To explore the physical meaning and implications of this stochastic
regime in relation to both classical and quantum gravity, we find it useful to
take the view that semiclassical gravity is mesoscopic physics and that general
relativity is the hydrodynamic limit of certain spacetime quantum
substructures. Three basic issues - stochasticity, collectivity, correlations-
and three processes - dissipation, fluctuations, decoherence- underscore the
transformation from quantum micro structure and interaction to the emergence of
classical macro structure and dynamics. We discuss ways to probe into the high
energy activity from below and make two suggestions: via effective field theory
and the correlation hierarchy. We discuss how stochastic behavior at low energy
in an effective theory and how correlation noise associated with coarse-grained
higher correlation functions in an interacting quantum field could carry
nontrivial information about the high energy sector. Finally we describe
processes deemed important at the Planck scale, including tunneling and pair
creation, wave scattering in random geometry, growth of fluctuations and forms,
Planck scale resonance states, and spacetime foams.
