Over the past 20 years, the field of medical image registration has significantly advanced from multi-modal image fusion to highly non-linear, deformable image registration for a wide range of medical applications and imaging modalities, involving the compensation and analysis of physiological organ motion or of tissue changes due to growth or disease patterns. While the original focus of image registration has predominantly been on correcting for rigid-body motion of brain image volumes acquired at different scanning sessions, often with different modalities, the advent of dedicated longitudinal and cross-sectional brain studies soon necessitated the development of more sophisticated methods that are able to detect and measure local structural or functional changes, or group differences. Moving outside of the brain, cine imaging and dynamic imaging required the development of deformable image registration to directly measure or compensate for local tissue motion. Since then, deformable image registration has become a general enabling technology. In this work we will present our own contributions to the state-of-the-art in deformable multi-modal fusion and complex motion modelling, and then discuss remaining challenges and provide future perspectives to the field.