Our conventional picture of wave functions living in an exponentially large Hilbert space is both impractical for solving many particle systems and conceptually lacking: in recent years we have come to understand that physical states of matter live in an infinitesimal corner of Hilbert space, characterized primarily by low entanglement. Tensor networks are the natural language to express low entanglement wave functions, giving an exponentially compressed description of ground states. The density matrix renormalization group (DMRG) and other tensor network algorithms have had tremendous success in simulating quantum lattice models. The key challenge in translating these methods to electronic structure is the need to represent continuum space in an efficient way. After an introduction to tensor networks, I’ll present a new DMRG-based approach suitable for the electronic structure of long molecules. Our sliced-basis DMRG method produces near-exact ground states within its basis, and has a computation time which is linear in the length of the molecule. We are implementing SBDMRG for chains of hydrogen atoms, where we have been able to simulate up to 1000 atoms in a minimal basis.