I have never ridden one (and I really want to ;-) ), but I've heard mixed reports on hills. You can push against the back of the seat, but you lose the advantage of using your weight on the pedals. Can anyone comment on what it's like for difficult hills? I have lots of gradients over 20% here and one of the hills I ride has a 30% section!

What BenFrantzDale said, plus: my old recumbent was front-wheel driven, but most of the weight was born by the rear-wheel.

So yes, I had problems on hills, because there was not enough weight on the driven wheel.

But mine was a very special kind of recumbent bikes, without a classic handlebar and instead steered with the feet. Most recumbents are driven on the rearwheel.

For the curious: I used to ride a flevo racer with a very unique steering mechanism. (See eg https://www.youtube.com/watch?v=eyTP5I8hv5Q)

It's a very curious bike to ride, with a long learning curve.

I have never ridden one either but weight on the pedals shouldn't matter. If you push down on a pedal as you extend your leg leaving your body at a constant height, that should be the same work as pushing just as hard over just as far against a seat. I'm sure there are subtleties – you can push more than your weight against a seat but a seat absorbs energy – but to first order it should be a wash.

I'm skeptical. When you're up out of the pedals and sprinting on a bike, you are transmitting an awful lot of energy. I don't quite see being able to push quite so hard when sat down.

One way of thinking about it is that work is force times distance, so if you aren't moving WRT the bike, and push just as far work goes by force. Assuming you don't have toe clips and so aren't pulling up with one foot while you push down with the other, then at most you can push down with your body weight. (You could push harder but that would leave your body accelerating up at the end of the stroke.)

You're thinking about it from a physics point of view, which is kind of abstract, and possibly not considering all the movement involved. I'm thinking about it from the point of sprinting for the finish line at a race last Sunday. I really don't think I could have brought the same force to bear while sitting down.

Also: modern bikes have clipless pedals, not toe clips.

Maximum force doesn't matter too much. Change gears, and you can always trade force for distance to get the same energy.