The Delivery Manager includes some analytics on the success rate of your campaigns. You can view the stats by clicking on the analytics icon in the 'Statistics' column:
For Automated campaigns, you will be able to view stats for both active and inactive campaigns. These are all-time stats reflecting all emails that have been sent for that particular campaign since it was first activated. For Manual campaigns, you can view stats for sent campaigns - these will reflect the sending for that one particular campaign.
The Statistics popup shows the number of attempted emails sent, and how many were successful or failed. For the successfully sent emails, you can also see the open rate. For failed emails, you will be able to see the reason they failed, for example if they bounced, were previously unsubscribed, or were stopped by the duplication rule: