One particularly attractive solution in automotive industry, where lightweight materials play an increasingly dominant role, is the utilization of Shape Memory Alloy (SMA) actuation technology, renowned for its ability to achieve a remarkably high power-to-weight ratio, especially suited for compact and lightweight actuators. For these reasons, this study will first introduce the complex behavior and remarkable properties of shape memory alloys (SMAs). Recognizing the importance of having a mathematical model to implement a control algorithm that can enhance the performance of these materials, a comprehensive overview of existing models and control strategies for SMAs will be provided. Next, various application sectors of SMAs will be explored, with a particular focus on the automotive industry.