Deep learning is a genre of machine learning that allows computational models to learn representations of data with multiple levels of abstraction using numerous processing layers. A distinctive feature of deep learning, compared with conventional machine learning methods, is that it can generate appropriate models for tasks directly from the raw data, removing the need for human-led feature extraction. Medical images are particularly suited for deep learning applications. Deep learning techniques have already demonstrated high performance in the detection of diabetic retinopathy on fundoscopic images and metastatic breast cancer cells on pathologic images. In radiology, deep learning has the opportunity to provide improved accuracy of image interpretation and diagnosis. Many groups are exploring the possibility of using deep learning-based applications to solve unmet clinical needs. In chest imaging, there has been a large effort to develop and apply computer-aided detection systems for the detection of lung nodules on chest radiographs and chest computed tomography. The essential limitation to computer-aided detection is an inability to learn from new information. To overcome these deficiencies, many groups have turned to deep learning approaches with promising results. In addition to nodule detection, interstitial lung disease recognition, lesion segmentation, diagnosis and patient outcomes have been addressed by deep learning approaches. The purpose of this review article was to cover the current state of the art for deep learning approaches and its limitations, and some of the potential impact on the field of radiology, with specific reference to chest imaging.