  The formation of a binary system surrounded by disks is the most common
outcome of stellar formation. Hence studying and understanding the formation
and the evolution of binary systems and associated disks is a cornerstone of
star formation science. Moreover, since the components within binary systems
are coeval and the sizes of their disks are fixed by the tidal truncation of
their companion, binary systems provide an ideal "laboratory" in which to study
disk evolution under well defined boundary conditions.
  In this paper, we review observations of several inner disk diagnostics in
multiple systems, including hydrogen emission lines (indicative of ongoing
accretion), $K-L$ and $K-N$ color excesses (evidence of warm inner disks), and
polarization (indicative of the relative orientations of the disks around each
component). We examine to what degree these properties are correlated within
binary systems and how this degree of correlation depends on parameters such as
separation and binary mass ratio. These findings will be interpreted both in
terms of models that treat each disk as an isolated reservoir and those in
which the disks are subject to re-supply from some form of circumbinary
reservoir, the observational evidence for which we will also critically review.
The planet forming potential of multiple star systems is discussed in terms of
the relative lifetimes of disks around single stars, binary primaries and
binary secondaries. Finally, we summarize several potentially revealing
observational problems and future projects that could provide further insight
into disk evolution in the coming decade
