You can already get this data in a zipfile of CSVs by doing a broadcast export using the action button next to a broadcast.
Soon you'll be able to view this data in the UI from the drill-down report for broadcasts and funnels.
To see the existing drill-down report, click on a broadcast name, or click "View Reporting" next to a funnel message.
You'll be able to click through to see the contacts who engaged with the message from that page once this feature goes in.