Up to 30 days after they’ve been sent or received
You can view received messages at your SMS Overview in the 'SMS' left-hand column of your Dashboard → 'SMS Overview' → 'Sent' tab.
More than 30 days after they’ve been sent or received
Within that overview, you can view your replies by selecting ‘Received’ out of the drop-down menu. You can select the month, message type (all messages, received, or sent), delimiter, and whatever extra fields you wish to export.