Book excerpt: Biophysical modelling of brain activity has a long and illustrious history and has recently profited from technological advances that furnish neuroimaging data at an unprecedented spatiotemporal resolution. Neuronal modelling is a very active area of research, with applications ranging from the characterization of neurobiological and cognitive processes, to constructing artificial brains in silico and building brain-machine interface and neuroprosthetic devices. Biophysical modelling has always benefited from interdisciplinary interactions between different and seemingly distant fields; ranging from mathematics and engineering to linguistics and psychology. This Research Topic aims to promote such interactions by promoting papers that contribute to a deeper understanding of neural activity as measured by fMRI or electrophysiology. In general, mean field models of neural activity can be divided into two classes: neural mass and neural field models. The main difference between these classes is that field models prescribe how a quantity characterizing neural activity (such as average depolarization of a neural population) evolves over both space and time as opposed to mass models, which characterize activity over time only; by assuming that all neurons in a population are located at (approximately) the same point. This Research Topic focuses on both classes of models and considers several aspects and their relative merits that: span from synapses to the whole brain; comparisons of their predictions with EEG and MEG spectra of spontaneous brain activity; evoked responses, seizures, and fitting data - to infer brain states and map physiological parameters.