You can view all emails or texts sent using automation by going to "Marketing>Automations" and then clicking the "Automation History" tab at the top.
Here you can see the Date the automation ran, the Trigger Condition, The action that happened when this automation ran, and the status.
If the automation is sent successfully, it will have a success message and will sometimes be labeled green:
If the automation fails, it will be red and have the reason why it failed: