I second Runtastic. It also does a lot more than just run logging if you do more than just running. I have been using it and it is great.https://www.runtastic.com/blog/en/hot-topics-and-reviews/runtastic-presents-new-features-for-ios-10/
"Start your activity directly on the first screen. Plus, get stats for distance, duration and pace at one glance. Oh, and you can see your current heart rate – which is synced in real time – on the main screen, too." (update coming soon).
It's a new API so I'm sure they all will in due time. Nike will for sure and I'd bet on all the other biggies as well. I'm on the beta program for iSmoothRun and know for fact he's implementing HR right now (BTW, iSmoothRun is the best app).Besides the stock app, do any running apps use the Apple Watch heart monitor to display your heart rate?
This doesn't track running, just your HR.
I thought most of the majors have done this since just after OS2: Runkeeper, Strava, MapMyRUn, Runtastic, iSmoothRun, etc. I have not used RK in months, but it did HR way back when.Besides the stock app, do any running apps use the Apple Watch heart monitor to display your heart rate?