  The odds theorem and the corresponding solution algorithm (odds algorithm)
are tools to solve a wide range of optimal stopping problems. Its generality
and tractability have caught much attention. (Google for instance "Bruss odds"
to obtain a quick overview.) Many extensions and modifications of the this
result have appeared since publication in~2000. This article reviews the
important gnew developments and applications in this field. The spectrum of
application comprises as different fields as secretary problems, more general
stopping problems, robotic maintenance problems, compassionate use clinical
trials and others. This review also includes a new contribution of our own.
