The status and some recent developments of continuum modeling for repetitive lattice structures are summarized. Discussion focuses on a number of aspects including definition of an effective substitute continuum; characterization of the continuum model; and the different approaches for generating the properties of the continuum, namely, the constitutive matrix, the matrix of mass densities, and the matrix of thermal coefficients. Also, a simple approach is presented for generating the analytic expressions and/or numerical values of the continuum properties. Sample numerical results are presented to demonstrate the effectiveness of the continuum modeling approach. Future directions of research on continuum modeling are identified. These include needed extensions and applications of continuum modeling as well as computational strategies and modeling techniques.