Superconducting nanostructures in the form of square and hexagonal nets of conductors in an external magnetic field are theoretically investigated. The superconducting transition temperatures as functions of the field as well as the intricate patterns of the order parameter and current are determined using a minimization technique of the Ginzburg-Landau free-energy expression. Experimental results and the relationships with the tight-binding model of electrons on a lattice and with other problems are discussed.