This review introduces a novel deformable image registration paradigm that exploits Markov random field formulation and powerful discrete optimization algorithms. We express deformable registration as a minimal cost graph problem, where nodes correspond to the deformation grid, a node's connectivity corresponds to regularization constraints, and labels correspond to 3D deformations. To cope with both iconic and geometric (landmark-based) registration, we introduce two graphical models, one for each subproblem. The two graphs share interconnected variables, leading to a modular, powerful, and flexible formulation that can account for arbitrary image-matching criteria, various local deformation models, and regularization constraints. To cope with the corresponding optimization problem, we adopt two optimization strategies: a computationally efficient one and a tight relaxation alternative. Promising results demonstrate the potential of this approach. Discrete methods are an important new trend in medical image registration, as they provide several improvements over the more traditional continuous methods. This is illustrated with several key examples where the presented framework outperforms existing general-purpose registration methods in terms of both performance and computational complexity. Our methods become of particular interest in applications where computation time is a critical issue, as in intraoperative imaging, or where the huge variation in data demands complex and application-specific matching criteria, as in large-scale multimodal population studies.