The non-archimedean SYZ fibration and the Minimal Model Program The SYZ fibration is a conjectural structure on maximally degenerating Calabi-Yau varieties that was predicted by Ströminger, Yau and Zaslow to give a geometric explanation for the phenomenon of Mirror Symmetry. Around 2000, Kontsevich and Soibelman have introduced the important idea that such a structure can be found in the context of non-archimedean geometry (Berkovich spaces). It turns out that the properties of the non-archimedean SYZ fibration are intimately connected with the Minimal Model Program, and that it forms a powerful heuristic to guess precise statements about the structure of minimal models of degenerations of Calabi-Yau varieties (even though, at this point, the proofs still heavily rely on MMP techniques). In my talks, I will explain this circle of ideas and give some examples of interactions between the non-archimedean SYZ fibration and the MMP, based on joint work with Mircea Mustata and Chenyang Xu