  The Bayesian statistical paradigm provides a principled and coherent approach
to probabilistic forecasting. Uncertainty about all unknowns that characterize
any forecasting problem -- model, parameters, latent states -- is able to be
quantified explicitly, and factored into the forecast distribution via the
process of integration or averaging. Allied with the elegance of the method,
Bayesian forecasting is now underpinned by the burgeoning field of Bayesian
computation, which enables Bayesian forecasts to be produced for virtually any
problem, no matter how large, or complex. The current state of play in Bayesian
forecasting in economics and finance is the subject of this review. The aim is
to provide the reader with an overview of modern approaches to the field, set
in some historical context; and with sufficient computational detail given to
assist the reader with implementation.
