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Uphill, the transmission will figure it out (it will keep downshifting if it's losing speed) until it can hold speed or it fails. If it' a gas engine and struggling, don't be surprised if you need to run 3500-4500rpm on a steep grade.
Downhill is more critical. If you let it gain too much speed, you may not be able to get it back under control. A good starting point is to force it into the lowest gear you were in going up. It's a bit different, gas vs diesel. Most modern diesels will have some form of exhaust braking which can be quite powerful. Gas engines create engine braking by winding up the RPM but aren't quite as powerful but do still make a significant difference and you don't want to give up that benefit.
In either case, if the engine isn't keeping speed under control, use short hard braking to bring the speed down and then release and let the speed slowly creep up before repeating. This allows time for the brakes to cool between uses. If you just ride the brakes, they will heat up until they are literally red hot, then the brake fluid can boil causing brake fade.
