The purpose of this talk is to introduce the classification problem of partially hyperbolic diffeomorphisms in dimension 3 (including introducing the concept of partially hyperbolic diffeomorphisms and its relevance). The main goal will be to explain the importance of the understanding of foliations in 3-manifolds as well as pseudo-Anosov dynamics and hyperbolic geometry to this task. The talk will touch on work by many people, but focus on recent work joint with T. Barthelme, S. Fenley and S. Frankel.