This will be an informal talk about a class of equations that arise in various areas of applied probability, such as optimal stochastic control, stochastic differential games, and mathematical economics/finance, but are also related to stochastic analysis on manifolds and Karcher means. Formally, they resemble classical stochastic differential equations but come with a terminal condition instead of an initial one. This 'minor' difference leads to a class of significantly different problems, which require distinct techniques. Unlike SDEs, BSDEs are an active area of research. Indeed, while the one-dimensional case has been well understood for over 20 years, basic questions of existence and uniqueness about systems of BSDEs are still wide open.