Despite many debates in the first half of the twentieth century, it is now largely a truism that humans and other animals build models of their environments and use them for prediction and control. However, model-based (MB) reasoning presents severe computational challenges. Alternative, computationally simpler, model-free (MF) schemes have been suggested in the reinforcement learning literature, and have afforded influential accounts of behavioural and neural data. Here, we study the realization of MB calculations, and the ways that this might be woven together with MF values and evaluation methods. There are as yet mostly only hints in the literature as to the resulting tapestry, so we offer more preview than review.