This thesis studies representation learning for medical imaging data analysis. We propose a deep learning framework that is composed of data representation and feature learning. The data representation module deals with challenges from the need to analyze the various types of data from medical imaging. Examples of such data include 1D physiological signals, 2D high-resolution images and 3D human shape. The framework uses deep convolutional neural networks (CNN) and deep recurrent neural networks (RNN) for feature learning from the data representations. The framework starts from converting the various types of medical imaging data to 2D visual representations unanimously. Transfer learning is a technique for addressing data insufficiency problems in deep learning. With this technique, the framework uses deep CNNs pre-trained on large-scale 2D image sets to extract deep features from the data representations. In applications where the medical data are in a sequential form, the framework also integrates deep RNNs to conduct representation learning in spatial, spectral and temporal domains. We introduce the representation learning framework through selected tasks, including detecting cardiac murmurs from phonocardiograms (PCGs), recognizing masses and calcifications in mammograms, and locating anatomical landmarks on 3D human surface data. In the detection of cardiac murmurs, we have found a suitable data representation, which is computed from mel spectrograms within specific frequency ranges. Deep feature learning from the representations has achieved an F-score of 0.9767. When deployed to the detection of abnormalities in mammograms, the framework trains patch CNNs and builds abnormality detectors that outperform traditional approaches by a large margin. When applied to 3D human surface data, the proposed framework demonstrates that the learned representations are invariant to viewpoints. When applied to the surface data for locating landmarks, the framework finds optimal data representations and it has achieved human-level performance. In summary, we have proposed a deep representation learning framework and proved its effectiveness in medical imaging data analysis. Experimental results indicate that the framework serves as a guidance on effective representation learning for solving other problems from medical imaging data analysis using deep learning.