Data privacy and security are fundamental to deploying large language models (LLMs) in the finance sector, where protecting sensitive information is paramount. This chapter provides a deep dive into the critical aspects of data privacy and security for LLM operations, emphasizing strategies to safeguard data throughout the LLM lifecycle. It begins by discussing data anonymization techniques such as masking and encryption, which are essential for protecting personally identifiable information (PII) and maintaining compliance with data protection laws.