My rule of thumb is to average around 75 to 80% over the course of the run. When I’m running uphills my heart rate often goes above the 85% too but as you say, on the downhill your heart gets a well earned rest.
I think a lot depends on the length and grade of the hill. If you have a very steep hill, even a very fit person can reach 80% or more of their max heart rate just walking up it.
There is no shame in walking up a hill if your heart is doing 80%+ because you are still getting the aerobic benefit but you also need to run some of the hills to work your muscles. The running action needed for hills is different to the flat, so I think of hill running as being more about working the muscles than for it’s aerobic benefit.

Cheers

I also like to monitor my runs via heartrate, but one of the issues I have is that my training courses have quite a few hills. Hence my heartrate tends to stay well below 80% max on downhills, but frankly sometimes I’d have to break into a walk to keep it below 80% on the uphills, and I often let it go up to 85%+. So do you think it OK to *average* no more than 80% over the entire run, or do you rather think its better to avoid going over 80% at all (apart from during occasional anaerobic workouts)?