For most people, statistical forecasting means modelling time series using the methods described by Box and Jenkins (1970). A Box and Jenkins model requires a large number of known data points before it can be properly chosen and, since it cannot be changed without again observing another batch of input, is only of use if the data conforms in the future to the chosen model. This means that this style of forecasting is essentially rigid, unadaptable and of limited use in practice. This paper sets out, with the aid of the examples, the essentials and some applications of Bayesian forecasting as developed by Harrison and Stevens (1976).