Machine learning has great potentials to improve the entire medical imaging pipeline, providing support for clinical decision making and computer-aided diagnosis. This thesis mainly focuses on developing machine learning methods for the improvement of magnetic resonance (MR) image reconstruction and analysis, specifically on dynamic MR image reconstruction, image registration and segmentation. Firstly, we propose to tackle the white matter hyperintensity (WMH) segmentation problem present in elderly subjects or patients with vascular diseases. A two-step framework consisting of (semi-)supervised large margin based algorithms is proposed, where both common features shared across subjects and individual-specific information from target subject are considered and utilised. To further improve the segmentation and differentiate WMHs and stroke lesions, a deep learning based model, uResNet, is proposed. It combines the effective U-net architecture with residual elements, and considers a sampling strategy for imbalanced data. Experiments demonstrate its better performance than other competing methods. Secondly, we propose to address the problem of dynamic MRI reconstruction from highly undersampled k-space data. A convolutional recurrent neural network architecture (CRNN-MRI) is developed, where it embeds the iterative optimisation process in a learning setting and exploits the temporal redundancies of cardiac sequences. As a complement, a k-t NEXT network is presented to recover the signals in both x-f and image domains alternatingly. We show that our proposed models can effectively reconstruct high quality cardiac MRI at high acceleration factors. Finally, deep learning approaches for image registration and its applications are investigated. A joint learning framework for cardiac segmentation and motion estimation is proposed, which can provide multi-task predictions simultaneously. This motion estimation method is further extended for multi-modal deformable registration, in which it proposes to embed multi-modal images onto a common latent shape domain via disentangled representations. Experimental results indicate their competing performance and faster registration speed compared to other conventional methods.