In this paper we propose a new method for abnormality detection in medical images which is based on the notion of medical saliency. The proposed method is general and is suitable for a variety of tasks related to detection of: 1) lesions and microcalcifications (MCC) in mammographic images, 2) stenoses in angiographic images, 3) lesions found in magnetic resonance (MRI) images of brain. The main idea of our approach is that abnormalities manifest as rare events, that is, as salient areas compared to normal tissues. We define the notion of medical saliency by combining local patch information from the lightness channel with geometric shape local descriptors. We demonstrate the efficacy of the proposed method by applying it to various modalities, and to various abnormality detection problems. Promising results are demonstrated for detection of MCC and of masses in mammographic images, detection of stenoses in angiography images, and detection of lesions in brain MRI. We also demonstrate how the proposed automatic abnormality detection method can be combined with a system that performs supervised classification of mammogram images into benign or malignant/premalignant MCC's. We use a well known DDSM mammogram database for the experiment on MCC classification, and obtain 80% accuracy in classifying images containing premalignant MCC versus benign ones. In contrast to supervised detection methods, the proposed approach does not rely on ground truth markings, and, as such, is very attractive and applicable for big corpus image data processing.