While we do not currently support deleting Contacts or Conversations permanently, we do provide the options to Filter your Conversation List and/or Archive your contacts.
Filtering your Conversation List allows you to tidy up your queue by selecting the most relevant view to you - you can view only Conversations that are Unresolved, those that are Claimed by / Assigned to you, or those that are new (unassigned) and Claimed by you. You can read more about filtering here.
Archiving a Contact will hide them from your main Address Book, and will hide any Conversations with that contact from the Conversation List. You can find out how to Archive your contacts by clicking here.
Watch the video tutorial on Using the Address Book here.