Recent developments in language modeling have increased their use in various applications and domains. Language models, often trained on sensitive data, can memorize and disclose this information during privacy attacks, raising concerns about protecting individuals' privacy rights. Preserving privacy in language models has become a crucial area of research, as privacy is one of the fundamental human rights. Despite its significance, understanding of how much privacy risk these language models possess and how it can be mitigated is still limited. This research addresses this by providing a comprehensive study of the privacy-preserving language modeling approaches. This study gives an in-depth overview of these approaches, highlights their strengths, and investigates their limitations. The outcomes of this study contribute to the ongoing research on privacy-preserving language modeling, providing valuable insights and outlining future research directions.