This workshop, sponsored by AIM and the NSF, will focus on connections between two kinds of inner models for Set Theory. The first is the well studied family of extender models, i.e. fine-structural models designed to contain large cardinals by incorporating extender sequences. The second is the new family of inner models, e.g. the aa-model, arising from extended logics, which has the potential to bring completely new insights into set theory. The area of properties of the new inner models as well as connections between the two kinds of inner models abounds in open problems and the forthcoming workshop provides an ideal opportunity for trying to solve them.