You can view the SMS status via the Dashboard and inside a contact record.  See examples below of Delivered SMS messages:

Here is a list of ALL the SMS status categories and what they mean:

'QUEUED' means the message is queued to be sent.

‘RECEIVED’ means that the gateway has received the message

‘SENT’ will mean that the message has been sent

'ACCEPTED' means that the SMS message has been accepted by the operator – and will be delivered to the handset when it is available

‘DELIVERED’ when we have received acknowledgement back from the handset that it has been delivered

'FAILED'  - this means that the SMS message was sent to the network – and the network has responded to say that it is not possible to deliver the message as the number is no longer in use – these messages are charged for as the message was sent.