Rate-splitting multiple access (RSMA) has emerged as a promising enabling technique for next generation wireless communications. Its unique structure and powerful interference management capability has brought new challenges and opportunities to safeguarding communications at the physical layer. In this article, we review security issues in the presence of internal and external eavesdroppers, respectively. Some mainstream techniques for addressing the introduced security concerns are presented. The role of optimizing the successive interference cancellation (SIC) decoding order in securing RSMA is further discussed explicitly. Finally, some open problems and research directions are envisioned.