Ultrasonography is a prominent method for screening thyroid tumors due to its safety, ease of use, and cost-effectiveness. However, the presence of speckle noise and other artifacts in ultrasound images can complicate the early detection of thyroid abnormalities, posing challenges for radiologists. Over the past three decades, researchers have actively sought to address these limitations and enhance the diagnostic capabilities of ultrasound images in evaluating thyroid tissue. This study presents a comprehensive review of various computer-aided diagnosis (CAD) systems specifically designed for the classification of thyroid tumor ultrasound (TTUS) images. The review encompasses a wide array of topics, including datasets utilized in research, despeckling algorithms that improve image quality, segmentation techniques that identify relevant areas of interest, and methods for feature extraction and selection that enhance classification accuracy. Additionally, the assessment parameters used to evaluate the performance of these systems are discussed, along with the classification algorithms employed to differentiate between benign and malignant tumors. Through this exhaustive analysis, the study highlights the achievements made in the field while also acknowledging the challenges that remain. Furthermore, it aims to provide a roadmap for future researchers interested in developing and refining CAD systems for thyroid tumor characterization, ultimately improving the diagnostic process and patient outcomes.