The past decade has witnessed a renewed interest in cortical local field potentials (LFPs) - that is, extracellularly recorded potentials with frequencies of up to approximately 500 Hz. This is due to both the advent of multielectrodes, which has enabled recording of LFPs at tens to hundreds of sites simultaneously, and the insight that LFPs offer a unique window into key integrative synaptic processes in cortical populations. However, owing to its numerous potential neural sources, the LFP is more difficult to interpret than are spikes. Careful mathematical modelling and analysis are needed to take full advantage of the opportunities that this signal offers in understanding signal processing in cortical circuits and, ultimately, the neural basis of perception and cognition.