As the customer is in center of business, accessing the communication history of a customer helps us serve better and helps us to get the good customer feedback for the service provided. The communication history can be found below the customer information; this includes not only the chat history but you can attach document to each message.
Click on the NEW MESSAGE button to compose a message to customer, you can enter the message, at the same time Odoo ask you to add them on the follower list. Followers are getting notified by email when you send messages, customer will get notify by email in their email box, look at the following email how email looks like in customer mailbox sent form Odoo:
When customer replies you on the same email, you will get notify in chatter below the customer information: