The aim of this talk is to suggest a new way of modeling neural tissue, not as a network, but instead as a three-dimensional continuum, partitioned by cell membranes into neurons, glia, and extracellular space. The fundamental equations of such a system are the 3D drift-diffusion equations for the various ions, neurotransmitters, and neuromodulators of the tissue, coupled to the Poisson equation for the electrical potential, with internal boundary (jump) conditions at cell membranes. We do not propose to homogenize these equations, but instead to solve them on the detailed, intricate geometry of the actual neuronal and glial cytoarchitecture. Because of a small parameter, the ratio of the Debye length to a typical cellular dimension, we are led to consider the limiting case known as electroneutrality, in which space charge is confined to thin layers near membranes, with the rest of the system being electrically neutral. An interesting complication here is that the ionic composition of the space charge layers enters into the boundary conditions and therefore needs to be determined. Boundary conditions across membranes involve the traditional Hodgkin-Huxley type equations for a membrane patch, taking into account the local densities of the different channel types. This talk will focus on the mathematical formulation of the problem, some preliminary numerical results, and a discussion of what it would take to do computational neuroscience this way.