This work introduces novel methods in the field of deformable image registration, both classical and learning-based. A central theme of the work is leveraging Reproducing Kernel Hilbert Space theory as a powerful regularization framework for dense displacement fields that are estimated via image registration. The first part of this work pursues this in the classical image registration regime, and advances on free form deformation methods by generalizing splines to arbitrary, spatially varying positive semi-definite ker-nels. Two algorithms that use this methodology are proposed, implemented, and tested, and experiments demonstrate the improvement in registration performance compared to contemporary classical methods. The second part of this work moves on to the trending field of learning-based image registration, which leverages deep learning architectures such as spatial transformer layers and U-nets. In this part we propose a modular, meta-regularization strategy to improve upon state of the art methods. This is done via estab-lishing a connection between multiplying by large Gram kernel matrices and convolution with special small matrices that are radially symmetric and positive semi-definite. As this complexity reduction bypasses the quadratic barrier of kernel methods, we then demonstrate how neural networks can be trained to learn such kernels efficiently, while jointly learning how to register. Numerous experiments on three datasets, includ-ing controlled and real displacements, are conducted to test this method under a variety of scenarios. An ablation analysis as well as statistical tests of significance are carried out to demonstrate the efficacy of the proposed method.