In this report we present the most important results of our recent analysis (Kupriyanov and Likharev 1990) of the Josephson effect in both the natural (intergrain) and artificial junctions using high-Tc superconductors (HTS). A comparison of the experimental data with the BCS-based theories of the Josephson effect in various tunnel-junction-type and weak-link-type structures has been carried out. The main conclusion is that the data presently available do not enable one to either confirm or reject the theories, and thus to reveal possible deviations of the real microscopic mechanism of the high-Tc superconductivity from the BCS mechanism. We suggest several experiments which would be more fruitful for this purpose, as well as for finding ways of reproducible fabrication of practically useful Josephson junctions.