From your teacher homepage, you can see a quick overview of what's going on in each of your classes with the Class Activity feature. Just click Show Activity to see more details.
The Class Activity feature shows the following:
Late assignment submissions since the last time you viewed the gradebook
The most recently due assignment(s) within the past two weeks
The next assignment(s) due (along with its due date, the number of students assigned, and the number of students who have completed the assignment)
You can click on any of the above assignment names to view its results.
If you do not the see "Show Activity" link on your homepage, then there have been none of the above updates since your last visit.