Synaptic neurotransmission is necessary but does not sufficiently explain superior cognitive faculties. Growing evidence has shown that neuron–astroglial chemical crosstalk plays a critical role in the processing of information, computation, and memory. In addition to chemical and electrical communication among neurons and between neurons and astrocytes, other nonsynaptic mechanisms called ephaptic interactions can contribute to the neuronal synchronization from different brain regions involved in the processing of information. New research on brain astrocytes has clearly shown that the membrane potential of these cells remains very stable among neighboring and distant astrocytes due to the marked bioelectric coupling between them through gap junctions. This finding raises the possibility that the neocortical astroglial network exerts a guiding template modulating the excitability and synchronization of trillions of neurons by astroglial Ca2+-associated bioelectromagnetic interactions. We propose that bioelectric and biomagnetic fields of the astroglial network equalize extracellular local field potentials (LFPs) and associated local magnetic field potentials (LMFPs) in the cortical layers of the brain areas involved in the processing of information, contributing to the adequate and coherent integration of external and internal signals. This article reviews the current knowledge of ephaptic interactions in the cerebral cortex and proposes that the isopotentiality of cortical astrocytes is a prerequisite for the maintenance of the bioelectromagnetic crosstalk between neurons and astrocytes in the neocortex.