I've heard people say that to climb a hill on a unicycle, you have to lean "into" the slope. Initially I thought that they were referring to a perceived forward lean, as opposed to a real one. That would then be a mental effect caused by the slope biasing your sense of verticalness, similar to how lake surfaces on a mountain side seem to "lean into" the slope. 

Later I have come to realise that it is not enough if the uni frame is vertical, and that there has to be a real physical forward lean. This is because your centre of gravity should be above the tyre contact point in order to have a constant speed. But the tyre contact point is positioned forward (with respect to the centre line) if you are on an upslope! The picture will explain this better. (The centre of gravity is high up since most mass is in the rider.) 

I have found that deliberately taking this effect into account, has helped me in hill climbing. 

Similarly, for going downhill you have to lean back into the slope. You can view the same picture with no modifications to illustrate that. Just imagine the uni is riding down.