You can view your conversation history with a contact on the Contact Details view by going to the Contacts page and clicking an individual contact from the list.
You can also use the dropdown menus on the Contact Details view to manage tags, notes, or view the most recent message in your conversations with the contact.
Tip: To view the most recent message in your 1:1 conversation with a contact, use the Your Conversations dropdown menu. For multi-user inboxes, you can view the most recent message in an assigned conversation under the Other Conversations dropdown.