Electrical signals from the cortical surface of animals were recorded as early as 1875 (REF. 1), 50 years before the advent of electroencephalography (EEG) 2 . Subsequent work revealed that the high-frequency part (above ~500 Hz) of the recorded potentials provides informa- tion about the spiking activity of neurons located around the electrode 3 . By contrast, the part of the signal that has frequencies below ~500 Hz, the so-called ‘local field potential’ (LFP), was found more difficult to interpret in terms of the underlying neural activity. Although the introduction of current source density (CSD) analysis in the 1950s 4 rejuvenated the use of the LFP in the follow- ing decades 5–7 , interest decreased in the 1980s and 1990s, probably owing to the focus on new single-neuron tech- niques (for example, patch-clamp recordings) and on understanding the link between single-neuron activity and perception. Recently, the interest in LFPs has undergone a resur- gence. Key reasons are the growing capacity for stream- ing continuous data from multiple electrodes and the development of multicontact electrodes for high-density recordings across areas and laminae 8–12 . Further, the LFP captures key integrative synaptic processes that can- not be measured by observing the spiking activity of a few neurons alone. Several studies have used LFPs to investigate cortical network mechanisms involved in sensory processing 13–30 , motor planning 31,32 and higher cognitive processes, including attention, memory and perception 33–37 . The LFP is also a promising signal for steering neuroprosthetic devices 38–41 and for monitoring neural activity in human recordings 42 because they are more easily and stably recorded in chronic settings than are spikes. However, the use of the LFP signal comes with an important caveat. Because multiple neuronal processes contribute to the LFP, the signal is inherently ambigu- ous and more difficult to interpret than spikes. Here, we argue that this ambiguity can, at least in part, be resolved by developing computational methods of analysis and modelling that are able to disambiguate the different neural contributions to the LFP. Developing such math- ematical tools is a thus a key priority of systems-level computational neuroscience. To achieve this goal, it is crucial to have a good understanding of the ‘measurement physics’ of LFPs — that is, the link between neural activity and what is measured. The past decade has seen the refinement of a well-founded biophysical forward-modelling scheme that is based on volume conductor theory 43,44 to incorporate detailed reconstructed neuronal morphologies in precise calculations of extracellular potentials — both spikes 45–52 and LFPs 19,49,50,53–56 . (The word ‘forward’ denotes that the extracellular potentials are modelled from neural transmembrane currents; inverse modelling, by contrast, estimates neural currents from recorded potentials.) By using this tool, systematic investigations of the link between the recorded LFPs and various types of under- lying neural activity can be pursued, and realistic data for the development and validation of methods for LFP analysis can be produced 12,49,57,58 . Modelling and analysis of local field potentials for studying the function of cortical circuits Gaute T. Einevoll 1 , Christoph Kayser 2,3, , Nikos K. Logothetis 4,5 and Stefano Panzeri 2,6 Abstract | The past decade has witnessed a renewed interest in cortical local field potentials (LFPs) — that is, extracellularly recorded potentials with frequencies of up to ~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. 1 Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, 1432 Ås, Norway. 2 Institute of Neuroscience and Psychology, University of Glasgow, Glasgow, G12 8QB, UK. 3 Bernstein Center for Computational Neuroscience, 72076 Tübingen, Germany. 4 Max Planck Institute for Biological Cybernetics, Spemannstrasse 38, 72076 Tübingen, Germany. 5 Division of Imaging Science and Biomedical Engineering, University of Manchester, Manchester, M13 9PT, UK. 6 Center for Neuroscience and Cognitive Systems, Istituto Italiano di Tecnologia, Via Bettini 31, 38068 Rovereto, Italy. Correspondence to G.T.E. and S.P.  e-mails: Gaute.Einevoll@umb.no; Stefano.Panzeri@glasgow.ac. uk doi:10.1038/nrn3599 REVIEWS 770 | NOVEMBER 2013 | VOLUME 14 www.nature.com/reviews/neuro © 2013 Macmillan Publishers Limited. All rights reserved