Machine learning is the backbone of artificial intelligence and it is based on the learning aspect. A key step in the transition from machine to deep learning is representation learning. Deep learning is a method of representation learning with multiple levels of representation that transforms raw data through multiple levels and creates abstractions that transform data into a simpler form. Deep learning is based on artificial neural networks or set of algorithms that mimic the mechanism of a biological neuron. Convolutional neural networks are most commonly used in radiology and they have a network structure like images and serve for adaptive learning of spatial features and pattern recognition. Breast cancer is the most common malignancy in the female population. Mammography is a screening method that is used for the detection of breast cancer. The aim of this paper is to systematically review the literature to show the basic principle of computer-aided diagnosis in mammography and to show it's performance. A system of computer-aided diagnosis can be integrated within the workstations of the mammography device to help radiologists in diagnostic interpretation with high efficiency. Mammography is analyzed in several steps, the first step is image pre-processing, followed by segmentation, extraction of features and it ends with their classification into benign or malignant entity. The implementation of deep learning in computer-aided diagnosis enables highly sensitive, highly specific and diagnostically reliable classification of breast microcalcifications and assessment of breast density. Various studies have also shown that the incorporation of a deep learning algorithm in the interpretation of mammography has resulted in approximate and/or better performance compared to the radiologist who independently interprets the findings. Those studies present early evidence that confirms the ability of artificial intelligence for integration within clinical systems.