This paper describes how the elements of the SP theory (Wolff, 2003a) may be realised with neural structures and processes. To the extent that this is successful, the insights that have been achieved in the SP theory - the integration and simplification of a range of phenomena in perception and cognition - may be incorporated in a neural view of brain function. These proposals may be seen as a development of Hebb's (1949) concept of a 'cell assembly'. By contrast with that concept and variants of it, the version described in this paper proposes that any one neuron can belong in one assembly and only one assembly. A distinctive feature of the present proposals is that any neuron or cluster of neurons within a cell assembly may serve as a proxy or reference for another cell assembly or class of cell assemblies. This device provides solutions to many of the problems associated with cell assemblies, it allows information to be stored in a compressed form, and it provides a robust mechanism by which assemblies may be connected to form hierarchies, grammars and other kinds of knowledge structure. Drawing on insights derived from the SP theory, the paper also describes how unsupervised learning may be achieved with neural structures and processes. This theory of learning overcomes weaknesses in the Hebbian concept of learning and it is, at the same time, compatible with the observations that Hebb's theory was designed to explain.