When visiting a recipient's Contact record, you should be able to see a history of past email campaigns that recipient has received. If you don't, here's a quick guide to troubleshooting.
1) Ensure that the Contact page layout has the Campaign History related list on it
The record of emails sent to recipients are stored as Campaign Member records in Salesforce, so to display these Campaign Member records on the Contact object, you'll need to make sure that the Campaign History related list is displayed on the Contact page layout.
Happy emailing!