How to add an email or domain on the client's suppression list?

To add an email address or a whole domain to the client's suppression list, click on the Client's tab. Beside the client's name, choose the Suppression button.

Add emails or entire domains of existing customers (or conversations) here and they will be automatically suppressed from any campaigns.

Don't forget to Save after adding the email or domain.

UPDATE: There is now a new way to add a contact or domain to the suppression list, read more of it here.