Underwater Acoustic Sensor Networks (UASNs) are an important technical means to explore the ocean realm. However, most UASNs rely on hardware infrastructures with poor flexibility and versatility. The systems typically deploy in a redundant manner, which not only leads to waste but also causes serious signal interference due to multiple noises in designated underwater regions. Software-Defined Networking (SDN) is a novel network paradigm, which provides an innovative approach to improve flexibility and reduce development risks greatly. Although SDN and UASNs are hot topics, there are currently few studies built on both. In this paper, we provide a comprehensive review on the advances in software-defined UASNs. First, we briefly present the background, and then we review the progress of the Software-Defined Radio (SDR), Cognitive Radio (CR), and SDN. Next, we introduce the current issues and potential research areas. Finally, we conclude the paper and present discussions. Based on this work, we hope to inspire more active studies and take a further step on software-defined UASNs with high performances.