You can see your progress for each route by checking the icon in the leftmost column of the route library:

The icons represent the following:

Play icon

You haven’t started the ride yet.

Progress icon

You’ve begun the ride but haven’t completed it.

Finish line icon

You’ve crossed the finish line, but it took more than one ride to complete the route.

Laurel wreath icon

You’ve successfully finished the route in a single ride. 

If you’re unsure of an icon’s meaning, hover your cursor over it to see a tooltip explanation:

Like other columns, you can sort the ‘Route Progress’ column by clicking on its head: