For any specific campaign, you will see an overview of the send. Details like the subject, send time and recipient list can be found here. You will also see a hyperlink to "View Email".
Once you click "View Email" you are redirected to an HTML email preview, which you can then download for your records. 
There may be cases when you can't see the "View Email" link, like below:
This is because the email was sent without a ContactMonkey email, created using our builder. Because it wasn't built using our tool, we can't track the HTML and get accurate metrics.
Have questions about the email builder? Reach out to your account manager.