This chapter reviews various elastic matching techniques for handwritten character recognition. Elastic matching is formulated as an optimization problem of planar matching, or pixel-to-pixel correspondence, between two character images under a certain matching model, such as affine and nonlinear. Use of elastic matching instead of rigid matching improves the robustness of recognition systems against geometric deformations in handwritten character images. In addition, the optimized matching represents the deformation of handwritten characters and thus is useful for statistical analysis of the deformation. This chapter argues the general property of elastic matching techniques and their classification by matching models and optimization strategies. It also argues various topics and future work related to elastic matching for emphasizing theoretical and practical importance of elastic matching.