Machine learning methods and in particular deep neural networks are revolutionizing the AI industry and have become a critical component of computing. Convolutional neural networks, designed to take advantage of structural information in images, have had significant impacts in visual pattern recognition within the computer vision community and is gaining wide acceptance among medical professionals. Numerous papers on using deep learning to diagnose a number of malignancies with radiological data achieved enhanced performances in various medical applications. Despite many successes of machine learning in medical images, studies using machine learning and convolutional neural networks to correlate molecular labels to imaging features for diseases such as clear cell renal cell carcinoma and glioblastoma multiforme are rare. In this study, we used convolutional neural networks to predict aggressiveness of clear cell renal cell carcinoma on computed tomography images and molecular subtypes of glioblastoma multiforme on magnetic resonance images. We tested several models using transfer-learning and training from scratch to find the best performer and utilized several visualization techniques to elucidate some of the inherent "black-box" characteristic of neural networks. This aspect is of particular importance clinically, but is not commonly done in medical image application studies, since it helps developers choose the right architecture for the specific problems and increase the effectiveness of the diagnostic system by its making decisions and actions more apparent to human users. Additionally we extracted a large set of quantitative imaging features that includes independent component analysis and used unsupervised consensus clustering to identify imaging subtypes of glioblastoma multiforme.