The present state of knowledge of the elastic properties of the ternary chalcopyrite compounds and some related materials is reviewed. Results of experimental elastic constant determinations are critically evaluated by comparing with other experimentally available material parameters that directly depend on the elastic constants. Possible reasons for existing discrepancies and obvious inconsistencies in the experimental data are discussed. The results of theoretical calculations of the elastic constants of these compounds based on different theoretical models and approaches are compared with experimental data and are assessed concerning achievable accuracy and reliability.