  A Machine can only learn if it is biased in some way. Typically the bias is
supplied by hand, for example through the choice of an appropriate set of
features. However, if the learning machine is embedded within an {\em
environment} of related tasks, then it can {\em learn} its own bias by learning
sufficiently many tasks from the environment. In this paper two models of bias
learning (or equivalently, learning to learn) are introduced and the main
theoretical results presented. The first model is a PAC-type model based on
empirical process theory, while the second is a hierarchical Bayes model.
