Thyroid cancer is common worldwide, with a rapid increase in prevalence across North America in recent years. While most patients present with palpable nodules through physical examination, a large number of small and medium-sized nodules are detected by ultrasound examination. Suspicious nodules are then sent for biopsy through fine needle aspiration. Since biopsies are invasive and sometimes inconclusive, various research groups have tried to develop computer-aided diagnosis systems. Earlier approaches along these lines relied on clinically relevant features that were manually identified by radiologists. With the recent success of artificial intelligence (AI), various new methods are being developed to identify these features in thyroid ultrasound automatically. In this paper, we present a systematic review of state-of-the-art on AI application in sonographic diagnosis of thyroid cancer. This review follows a methodology-based classification of the different techniques available for thyroid cancer diagnosis. With more than 50 papers included in this review, we reflect on the trends and challenges of the field of sonographic diagnosis of thyroid malignancies and potential of computer-aided diagnosis to increase the impact of ultrasound applications on the future of thyroid cancer diagnosis. Machine learning will continue to play a fundamental role in the development of future thyroid cancer diagnosis frameworks.