  We review the models and results of simulations of self-gravitating, gaseous
protoplanetary disks in binary star systems. These models have been calculated
by three different groups with three different computational methods, two
particle-based and one grid-based. We show that interactions with the companion
star can affect the temperature distribution and structural evolution of disks,
and discuss the implications for giant planet formation by gravitational
instability as well as by core accretion. Complete consensus has not been
reached yet on whether the formation of giant planets is promoted or suppressed
by tidal interactions with a companion star. While systems with binary
separations of order 100 AU or larger appear to behave more or less as in
isolation, systems with smaller separations exhibit an increased or decreased
susceptibility to fragmentation, depending on the details of thermodynamics, in
particular on the inclusion or absence of artificial viscosity, and on the
initial conditions. While code comparisons on identical problems need to be
carried out (some of which are already in progress) to decide which computer
models are more realistic, it is already clear that relatively close binary
systems, with separations of order 60 AU or less, should provide strong
constraints on how giant planets form in these systems.
