The inner model program is one of the central pillars of modern research in set theory. Grounded in Gödel’s work, it aims at reaching stronger and stronger canonical inner models for large cardinals. These inner models provide a controlled environment to study the structural behaviour of large cardinals and can be regarded as witnesses for their consistency. Their construction relies on a deep relationship with models of determinacy. But this relationship is facing serious obstacles, resulting in the failure of established methods even below a Woodin limit of Woodin cardinals. In this talk we will describe these obstacles as well as scenarios for solutions for a non-expert audience.