Email notifications have been enabled now within the forum.
This means that when you are sent a private message you will receive an email notification.
But these will only be sent if you are not currently on the website.
You can always control your email notifications via User Preferences.
And all emails contain a link like the one shown in this picture to take you directly there:
Yes - the forum was down for 6 minutes whilst we enabled this - small downtimes are required to enable certain improvements.