Two of the teachers' knowledge models most widely used in the literature are the Mathematical Knowledge for Teaching (MKT) and the Knowledge Quartet (KQ). We develop an analysis of the limitations of the knowledge required for teaching problem-solving published during 1990-2018 which includes these models. This analysis revealed that MKT takes neither the nature of the process nor the knowledge accumulated by problem-solving research into consideration. While the KQ issubject to similar omissions, its major drawback is element overlap. We conclude that the knowledge required to teach problem-solving is not clearly envisaged in the theoretical teachers' knowledge models analysed.