In this review, we focus on electrophysiology at the mesoscale—extracellular recordings via metal electrodes, open-gate field-effect transistors (OGFETs) or oxide-semiconductor FET (OSFET) integrated into large arrays, so-called microelectrode arrays (MEAs). This method enables simultaneous and long-term recordings of local field potentials (LFPs) and extracellular action potentials (EAPs) from a population of neurons at millisecond time scale. It also allows perturbing neuronal activity using electrical stimulation. As data obtained from in vivo and in vitro experiments are often very similar, the MEA technology, concepts, and applications we include here apply to both and will be helpful for scientists and engineers from either field. In particular, we explain the interface between the neuron and the electrode in order to understand how to interpret the recordings. We highlight trends in the development of complementary metal-oxide-semiconductor (CMOS) based high-density MEAs (HDMEAs). The advantages of HDMEAs include the capability to map neuronal activity at sub-cellular resolution, localize single cells, and to constrain full-compartmental neuron models.