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You can check the number of bounced emails your organization has had for a particular campaign by going to Services > Email Marketing: Campaigns. The list of your current campaigns opens.
To the far left right is the number of bounced emails. However, you can see that you also can review how many emails were sent for a particular campaign, how many were opened (this number does not reflect, of course, whether someone read it), how many clicked a link in the email, as well as any marked spam. You can also see if people unsubscribed. Because this list is a datatable, you can change the view or create a custom view. For instance, you can create a new view based only on the bounced emails from your campaigns.
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