Ultrasound imaging is the most widespread medical imaging modality for creating images of the human body in clinical practice. Tissue classification in ultrasound has been established as one of the most active research areas, driven by many important clinical applications. In this paper, we present a survey on ultrasound tissue classification, focusing on recent advances in this area. We start with a brief review on the main clinical applications. We then introduce the traditional approaches, where the existing research on feature extraction and classifier design are reviewed. As deep learning approaches becoming popular for medical image analysis, the recent deep learning methods for tissue classification are also introduced. We briefly discuss the FDA-cleared techniques being used clinically. We conclude with the discussion on the challenges and research focus in future.