How reminders works?

Sorry for being so stupid but I didn't get how reminders works. I set up reminder for a certain day. The day has come a nothing happened :-( No push notification, nothing when I started the app. So what is the reminder for?

I also didn't find a way to show list of reminders. There is no option in the menu :-(

Can anybody give me a tutorial how should reminders works and how to be notified when it reaches the day / odometer state ?