If you have enabled Two-Way SMS on your account, the responses to SMS's will create a thread that is available in the Inbox in your Web Portal. You will be able to view both read and unread messages, filters and custom views can also be created to filter through the messages as needed.
If you do not have Two-Way SMS enabled and your customer responds to the SMS, their responce will not be received as the SMS is sent via a No Reply system generated number.