Hippocampal 'place cells' systematically shift their phase of firing in relation to the theta rhythm as an animal traverses the 'place field'. These dynamics imply that the neural ensemble begins each theta cycle at a point in its state-space that might 'represent' the current location of the rat, but that the ensemble 'looks ahead' during the rest of the cycle. Phase precession could result from intrinsic cellular dynamics involving interference of two oscillators of different frequencies, or from network interactions, similar to Hebb's 'phase sequence' concept, involving asymmetric synaptic connections. Both models have difficulties accounting for all of the available experimental data, however. A hybrid model, in which the look-ahead phenomenon implied by phase precession originates in superficial entorhinal cortex by some form of interference mechanism and is enhanced in the hippocampus proper by asymmetric synaptic plasticity during sequence encoding, seems to be consistent with available data, but as yet there is no fully satisfactory theoretical account of this phenomenon. This review is part of the INMED/TINS special issue Physiogenic and pathogenic oscillations: the beauty and the beast, based on presentations at the annual INMED/TINS symposium (http://inmednet.com).