Strong-coupling models for the electronic structure of La 2 CuO 4 are derived from the local-density-functional results in two successive stages of renormalization. First, a three-band Hubbard model is derived with parameters explicitly calculated from first principles using a constrained density-functional approach and a mean-field fit to the Cu-O pdσ bands. Second, exact diagonalization studies of finite clusters within the three-band Hubbard model are used to select and map the low-energy spectra onto effective one-band Hamiltonians, eg, the Heisenberg, one-band Hubbard, or ‘‘t-t’-J’’model. At each stage, calculated observables are in quantitative agreement with experiment.