Both Group, and Blog/Feed pages have been enhanced to display their most recent activity.

So, for blogs and feeds: the most recent posts from a blog or feed; for groups – much more fun – a real-time aggregated feed from all the members of that group. Here’s an example for the UK Labour Party’s group.
You can also see that joining or leaving an open group – or applying to join a restricted group – is simply a matter of a single click.