Thyroid nodule is one of the common life-threatening diseases, and it had an increasing trend over the last years. Ultrasound imaging is a commonly used diagnostic method for detecting and characterizing thyroid nodules. However, assessing the entire slide images is time-consuming and challenging for the experts. For assessing ultrasound images in a meaningful manner, there is a need for automated, trustworthy, and objective approaches. The recent advancements in deep learning have revolutionized many aspects of computer-aided diagnosis (CAD) and image analysis tools that address the problem of diagnosing thyroid nodules. In this study, we explained the objectives of deep learning in thyroid cancer imaging and conducted a literature review on its potential, limits, and current application in this area. We gave an overview of recent progress in thyroid cancer diagnosis using deep learning methods and discussed various challenges and practical problems that might limit the growth of deep learning and its integration into clinical workflow.