We describe a method for articulated human detection and human pose estimation in static images based on a new representation of deformable part models. Rather than modeling articulation using a family of warped (rotated and foreshortened) templates, we use a mixture of small, non-oriented parts. We describe a general, flexible mixture model that jointly captures spatial relations between part locations and co-occurence relations between part mixtures, augmenting standard pictorial structure models that encode just spatial relations. Our models have several notable properties: (1) they efficiently model articulation by sharing computation across similar warps (2) they efficiently model an exponentially-large set of global mixtures through composition of local mixtures and (3) they capture the dependency of global geometry on local appearance (parts look different at different locations). When relations are tree-structured, our models can be efficiently optimized with dynamic programming. We introduce novel criteria for evaluating pose estimation and human detection, both separately and jointly. We show that currently-used evaluation criteria may conflate these two issues. We present experimental results on standard benchmarks that suggest our approach is the state-of-the-art system for pose estimation, improving past work on the challenging Parse and Buffy datasets, while being orders of magnitude faster.