Autonomous driving systems require accurate and reliable perception. However, adverse environments, such as rain, snow, and fog, can significantly degrade the performance of LiDAR and cameras. In contrast, 4D millimeter-wave (mmWave) radar not only provides 3D sensing and additional velocity measurements but also maintains robustness in challenging conditions, making it increasingly valuable for autonomous driving. Recently, research on 4D mmWave radar under adverse environments has been growing, but a comprehensive survey is still lacking. To bridge this gap, this survey comprehensively reviews the current research on 4D mmWave radar under adverse environments. First, we present an overview of existing 4D mmWave radar datasets encompassing diverse weather and lighting scenarios. Next, we analyze methods and models according to different adverse conditions. Finally, the challenges faced in current studies and potential future directions are discussed for advancing 4D mmWave radar applications in harsh environments. To the best of our knowledge, this is the first survey specifically focusing on 4D mmWave radar in adverse environments for autonomous driving.