At intermediate mass transfer rates, accretion disks in binary star systems undergo a thermally-driven limit cycle instability. This instability leads to outburst episodes when the disk is bright and the flow through the disk is rapid separated by long intervals when the disk is dim and the flow through it is low. This intrinsic outburst mechanism can help to understand a wide range of astrophysical phenomena from dwarf novae to soft X -ray transients involving white dwarf, neutron star, and black holes. and to a deeper understanding of the mechanism of angular transport and viscosity in the accretion disk.