  Collisional complexes, which are formed as intermediate states in molecular
collisions, are typically short-lived and decay within picoseconds. However, in
ultracold collisions involving bialkali molecules, complexes can live for
milliseconds, completely changing the collision dynamics. This can lead to
unexpected two-body loss in samples of nonreactive molecules. During the last
decade, such "sticky" collisons have been a major hindrance in the preparation
of dense and stable molecular samples, especially in the quantum-degenerate
regime. Currently, the behavior of the complexes is not fully understood. For
example, in some cases their lifetime has been measured to be many orders of
magnitude longer than recent models predict. This is not only an intriguing
problem in itself but also practically relevant, since understanding molecular
complexes may help to mitigate their detrimental effects. Here, we review the
recent experimental and theoretical progress in this field. We treat the case
of molecule-molecule as well as molecule-atom collisions.
