You can check if an email has been successfully delivered to a contact depending on how the email was sent.

Emails sent from the contact record page or from an automation will show on the contact record dashboard. Once an email has been delivered, tracking information will show below the email on the note. The tracking information will say something like, 'Did not open', 'Opened 2 times, did not click' or something similar. If there is no reporting then Eagle has not received confirmation that the email has been successfully delivered.

There are detailed reports for email campaigns where you can see opens, clicks and other metrics. Please refer to the Email Reporting article for more information.