For reporting on Digital conversations these are currently available on 3 objects that provide different information to aid you in building your reports and dashboards.
Natterbox Conversation
The purpose of these reporting records are to act as the master record for each Digital conversation. Every time a new conversation is created this will create a record in Salesforce.
More information on the Natterbox Conversation object can be found here.
Natterbox Interaction
The purpose of these reporting records are to show what happened for each user (or customer) in the conversation during the set interval period. This is typically useful to understand trends in a conversation or agent performance.
More information on the Natterbox Interactions object can be found here.
Natterbox Wrap-Up
The purpose of these reporting records are for each time a User creates a Wrap-Up this will create a record in Salesforce for you to produce reports on. These are kept up to date if a User modifies or removes a Wrap-Up in the messaging interface.
More information on the Natterbox Wrap-Ups object can be found here.