  Variational quantum computing offers a flexible computational paradigm with
applications in diverse areas. However, a key obstacle to realizing their
potential is the Barren Plateau (BP) phenomenon. When a model exhibits a BP,
its parameter optimization landscape becomes exponentially flat and featureless
as the problem size increases. Importantly, all the moving pieces of an
algorithm -- choices of ansatz, initial state, observable, loss function and
hardware noise -- can lead to BPs when ill-suited. Due to the significant
impact of BPs on trainability, researchers have dedicated considerable effort
to develop theoretical and heuristic methods to understand and mitigate their
effects. As a result, the study of BPs has become a thriving area of research,
influencing and cross-fertilizing other fields such as quantum optimal control,
tensor networks, and learning theory. This article provides a comprehensive
review of the current understanding of the BP phenomenon.
