While we do not currently support permanently deleting Contacts or Conversation Histories, we do provide the ability to Filter your Conversation List and Archive your contacts.
You can tidy up your queue by filtering the Conversation List to the view that is most relevant to you. Set Status to Open to hide Resolved Conversations, and use Assigned to to narrow the list to Mine, Unassigned, or Mine + Unassigned. 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.