Nanosize pores can turn semimetallic graphene into a semiconductor and, from being impermeable, into the most efficient molecular-sieve membrane. However, scaling the pores down to the nanometer, while fulfilling the tight structural constraints imposed by applications, represents an enormous challenge for present top-down strategies. Here we report a bottom-up method to synthesize nanoporous graphene comprising an ordered array of pores separated by ribbons, which can be tuned down to the 1-nanometer range. The size, density, morphology, and chemical composition of the pores are defined with atomic precision by the design of the molecular precursors. Our electronic characterization further reveals a highly anisotropic electronic structure, where orthogonal one-dimensional electronic bands with an energy gap of similar to 1 electron volt coexist with confined pore states, making the nanoporous graphene a highly versatile semiconductor for simultaneous sieving and electrical sensing of molecular species.