Through the API it is possible to consult the status of each message or receive the status changes of any message sent in a URL. See the specific method in the instructions for each version of the API (SMS API support resources).
It is also possible to access the control panel (WebSMS application) with the username and password. In the account it is possible to see the information of the messages sent in the History section. More information on ¿How to check the status and data of a sent SMS? or Statuses of an SMS message.