The 820 gives you text/call/calendar/missed call/other notifications.
The 800 was the last 8xx computer that didn't. I can't say how they work on an 820 but on a 1000 a message shows up at the bottom of the screen that says "Text from Beth" or something; if you touch it, the text will display, if you touch outside of it or wait long enough it will go away. I assume emails will show the "preview" version of the message that's displayed in your phone's notification area. Haven't seen calendar alerts on the Edge yet so I can't comment on them. You can allow or block alerts from Facebook or Uber or anything else on your phone.