We present an integrated methodology for detecting, segmenting and classifying breast masses from mammograms with minimal user intervention. This is a long standing problem due to low signal-to-noise ratio in the visualisation of breast masses, combined with their large variability in terms of shape, size, appearance and location. We break the problem down into three stages: mass detection, mass segmentation, and mass classification. For the detection, we propose a cascade of deep learning methods to select hypotheses that are refined based on Bayesian optimisation. For the segmentation, we propose the use of deep structured output learning that is subsequently refined by a level set method. Finally, for the classification, we propose the use of a deep learning classifier, which is pre-trained with a regression to hand-crafted feature values and fine-tuned based on the annotations of the breast mass classification dataset. We test our proposed system on the publicly available INbreast dataset and compare the results with the current state-of-the-art methodologies. This evaluation shows that our system detects 90% of masses at 1 false positive per image, has a segmentation accuracy of around 0.85 (Dice index) on the correctly detected masses, and overall classifies masses as malignant or benign with sensitivity (Se) of 0.98 and specificity (Sp) of 0.7.