Your Inbox stores all incoming messages and replies sent from subscribers or people who text in to your Longcode.
Disable/enable email notifications - Login to your account, go to Account Settings, and scroll to the bottom of the page. Select or deselect "Email on Opt-in" (when someone joins any of your Lists), and "Email on Incoming Text" (when you receive a new Inbox message).
Disable/enable mobile app push notifications - Go to Account Settings (bottom right icon) in the Clearstream app. Select or deselect Opt-ins and/or Incoming Texts.