Vertebral body compression fractures are reliable early signs of osteoporosis. Though these fractures are visible on Computed Tomography (CT) images, they are frequently missed by radiologists in clinical settings. Prior research on automatic methods of vertebral fracture classification proves its reliable quality; however, existing methods provide hard-to-interpret outputs and sometimes fail to process cases with severe abnormalities such as highly pathological vertebrae or scoliosis. We propose a new two-step algorithm to localize the vertebral column in 3D CT images and then to simultaneously detect individual vertebrae and quantify fractures in 2D. We train neural networks for both steps using a simple 6-keypoints based annotation scheme, which corresponds precisely to current medical recommendations. Our algorithm has no exclusion criteria, processes 3D CT in 2 s on a single GPU and provides an intuitive and verifiable output. The method approaches expert-level performance and demonstrates state-of-the-art results in vertebrae 3D localization (the average error is 1 mm), vertebrae 2D detection (precision is 0.99, recall is 1), and fracture identification (ROC AUC at the patient level is 0.93).