We've gathered a bit more information on how push notifications on Windows Phone 7 series work. The notifications will come from Microsoft via a service offered free to developers. Our big question, though, was what the user experience will be like. From what we can tell, it will be "mixed' (pardon the pun).
Microsoft tell us that there won't be a "notification management app," which is to say that how notifications will surface is apparently going to differ app-by-app and user by user. Microsoft focused on the fact that many (or most) of the hubs will have a 'What's New' section where you'll be able to see new alerts. Hubs/apps that you've promoted to the Start screen will naturally display notifications in live tiles. Beyond that, though, it doesn't sound like we'll have an similar to Android or webOS, where you'll be able to see all your missed notifications and alerts in one place. We'll see if we're misinterpreting that when we speak with Microsoft one-on-one later.
On the bright side, from the demo we watched during the keynote today, it doesn't appear that notifications are 'interruptive,' so they won't force you to act on them before you get back to the work you're currently doing on the phone.