The richness of high-level cognitive and adaptive properties of the brain is reflected in the complexity of its anatomy and (electro)physiology. At the cellular level, evolution privileged for the central nervous system an analog distributed information storage and encoding, by plastic (graded) synapses and by their continuous temporal and spatial integration into firing rates. Beyond all-or-none action potentials, subthreshold synaptic and membrane electric activity in neurons disclose the details of single-neuron computations, neuronal identity and role, information processing and synaptic readout, as well as history-dependent dynamics of excitability and synaptic efficacy. The long-term experimental access to subthreshold activity of many neurons simultaneously, during behaviour and cognition, is then a requirement for the ultimate understanding of brain functions, its reverse engineering, as well as an unexplored alternative for neuroprosthetics.Project BRAINLEAP develops a breakthrough, revolutionary technological approach to explore cognition and plasticity in cortical neuronal networks, and preliminary applies it in vitro and in awake behaving rodents and primates. BRAINLEAP will enable simultaneous, long-term, and independent recording and stimulation of the electrical activity from hundreds of individual mammalian neurons, with a quality that in practice matches the intracellular configuration. By allowing one to record (and stimulate) for very long times, synaptic- and action-potentials from individual neurons, in the context of specific sensorimotor integration tasks, the leap we propose might ultimately shift current paradigms and theories, from spike-centred computation to its underlying subthreshold synaptic potentials computation.