  We consider particle systems (also known as point processes) on the line and
in the plane, and are particularly interested in "hole" events, when there are
no particles in a large disk (or some other domain). We survey the extensive
work on hole probabilities and the related large deviation principles (LDP),
which has been undertaken mostly in the last two decades. We mainly focus on
the recent applications of LDP-inspired techniques to the study of hole
probabilities, and the determination of the most likely configurations of
particles that have large holes.
  As an application of this approach, we illustrate how one can confirm some of
the predictions of Jancovici, Lebowitz, and Manificat for large fluctuation in
the number of points for the (two-dimensional) $\beta$-Ginibre ensembles. We
also discuss some possible directions for future investigations.
