"Pending" in PersistIQ means that your emails are currently being ready to add to the first step of the campaign. This can occur if you have a sending window set up. If you have a sending window set up in PersistIQ, your prospects will remain on "Pending" until the specified time to launch. If you are trying to add prospects outside of the sending window the emails will stay in "processing" till the sending window hits.
"Upcoming" means that the emails are ready to send on a specific day but they are not due just yet. It shows if the campaign has a manual (default) setup.
"Scheduled" means that the emails have been processed and are ready to send on the scheduled date. It is the same as "upcoming" but if you have an Auto Send it will say "scheduled". Keep in mind if you have Auto Send the emails will start sending as soon as the sending window hits. You won't need to do anything on your end.
"Due" in the manual campaign setup means that the email is ready to send and you need to click on "review email" and "send now" buttons to trigger the sending.
"Processing" means that emails are getting ready to be added to the first step of the campaign. If the sending window doesn't block the process the emails will be added to the first step within 15 minutes or less.