It has become common to publish large language models that have been trained on private datasets. However, large language models can memorize and leak individual training examples, which severely affects the privacy and security of private datasets. In this chapter, we will discuss training language models in Federated Learning and its privacy and security challenges of the training process. We introduce a novel concept of user-entity differential privacy (UeDP) to provide formal privacy protection simultaneously to both sensitive entities in textual data and data owners in learning natural language models (NLMs). To preserve UeDP, we developed a novel algorithm, called UeDP-Alg, optimizing the trade-off between privacy loss and model utility with a tight sensitivity bound derived from seamlessly combining user and sensitive entity sampling processes. An extensive theoretical analysis and evaluation show that our UeDP-Alg outperforms baseline approaches in model utility under the same privacy budget consumption on several NLM tasks, using benchmark datasets. The chapter will continue with discussion about extending UeDP to solve privacy problems in training large language models, including Federated Learning.