AbstractThis work reviews state of the art representative volume element (RVE) generation techniques for heterogeneous materials. To this end, we present a systematic classification considering a wide range of heterogeneous materials of engineering interest. Here, we divide heterogeneous solids into porous and non-porous media, with 0 < void volume fraction < 1 and void volume fraction = 0, respectively. Further subdivisions are realized based on various morphological features. The corresponding generation methods are classified into three categories: (i) experimental methods targeting reconstruction through experimental characterization of the microstructure, (ii) physics based methods targeting simulation of the physical process(es) responsible for the microstructure formation and evolution, and (iii) geometrical methods concentrating solely on mimicking the morphology (ignoring the physical basis of the microstructure formation process). These comprise of various mathematical tools such as digital image correlation, tessellation, random field generation, and differential equation solvers. For completeness, relevant up-to-date software tools, used at various stages of RVE generation – either commercial or open-source – are summarized. Considered methods are reviewed based on their efficiency and predictive performance with respect to geometrical and topological properties of the microstructures.