Simple, distributed and iterative algorithms, popularly known as message-passing, have become the architecture of choice for emerging infrastructure networks and the canonical behavioral model for natural networks. Therefore designing, as well as understanding, message-passing algorithms has become important.

The purpose of this survey is to describe the state-of-art of message-passing algorithms in the context of dynamic resource allocation in the presence of uncertainty, a problem that is central to operations research (OR) and management science (MS). Various directions for future research are described in this context as well as connections beyond OR and MS are explained. Through this survey, we hope to convey the opportunity presented to the OR and MS community to benefit from and contribute to the growing inter-disciplinary area of message-passing algorithms.