In the upper left corner of the UI, you will see either a) a finish line flag icon next to your distance left (configured to the units you specified in your Profile) for Races & Rides, or b) a rider-on-a-bicycle icon next to your distance gone for Maps & Paced Rides.
For activities with a known distance (Races & Rides), the distance in the upper left will count down. If it's an activity with an unknown distance (Maps & Paced Rides), it will count up.