  Chance-constrained programming (CCP) is one of the most difficult classes of
optimization problems that has attracted the attention of researchers since the
1950s. In this survey, we focus on cases when only a limited information on the
distribution is available, such as a sample from the distribution, or the
moments of the distribution. We first review recent developments in
mixed-integer linear formulations of chance-constrained programs that arise
from finite discrete distributions (or sample average approximation). We
highlight successful reformulations and decomposition techniques that enable
the solution of large-scale instances. We then review active research in
distributionally robust CCP, which is a framework to address the ambiguity in
the distribution of the random data. The focal point of our review is on
scalable formulations that can be readily implemented with state-of-the-art
optimization software. Furthermore, we highlight the prevalence of CCPs with a
review of applications across multiple domains.
