This dissertation explores innovative applications of diverse image registration techniques in the context of video coding and medical image analysis. Motion-compensated prediction is the key to video coding. Sophisticated motion-compensation technologies need to be integrated into future codecs to ensure its continual improvement. Previous works have explored alternatives to classical motion models that can only estimate translational movements in videos. But the cumulative rate-distortion performance has not been significant enough to see such approaches adopted in mainstream standards. In this thesis, an advanced motion compensation technique is presented that effectively predicts non-translational motion. A novel elastic motion model is derived for this purpose based on elastic image registration with 2-D cosine basis functions. To achieve superior performance, the proposed scheme takes advantage of larger macro-blocks with multi-level partitioning. Next, a novel block-partitioning scheme is introduced that attempts to slice the blocks based on motion-field discontinuity or geometry of edges rather than traditional predefined squares or rectangles. Both geometry-adaptive partitioning and higher-order elastic motion models are advanced coding techniques and can be considered as good candidates for future coders. However, it is vital that they are additive in performance, non-interfering and maintain justifiable complexity. Therefore, the elastic motion compensation platform has been extended by incorporating geometry-adaptive partitioning to attain even better compression. Finally, a new form of image registration, also known as 3D/2D registration is studied for analyzing relative movements in human joints from fluoroscopy images. This technology has many promising applications e.g. image-guided surgery, interventions and radiotherapy etc. However, precise measurement of out-of-plane movements remains a challenge for this to become a reality. In this study, a fast and accurate 3D/2D registration technique is put forward for kinematic analysis. The new algorithm takes advantage of a new multi-modal similarity measure called ‘sum of conditional variances’, a coarse-to-fine Laplacian of Gaussian filtering approach for robust gradient descent optimization and a novel technique for the analytic calculation of the required gradients for out-of-plane rotations. The accuracy and speed of the proposed method has been verified using clinical ‘gold-standard’ Roentgen Stereo Analysis (RSA).