I have seen competitive (amateur) cyclists with oval chainrings (front). What is the deal? Are they just for showing off, or is there a practical gain from it (different force transfer).
In theory they are more efficient.
Throughout the pedal stroke your leg doesn't give an equal amount of force - ideally you want to spend most of the time pushing down with the big thigh muscles and a minimum time in the horizontal movements at the top and bottom of the stroke.
Elliptical front cogs give you a more up-down leg motion, so more time with the big muscles and more power - not sure how much it actually works in practice, or how much practice it takes to make it work.
I cannot trot out the studies from memory now, so take my answer with a big grain of salt. Or as an invitation to do more in-depth research.
When I was actually researching these things several years ago, my conclusions were than the classic oval chainrings were ineffectual in whatever goal they were attempting to reach, while the newer Rotor system actually provided some small benefit on the order of 1-2% better average power.
It seems that right thing to strive for is minimizing the maximal force exerted by the muscles, because the maximal force is correlated with utilization of glycogen (the bigger the force exerted, the greater the proportion of glycogen burned via the inefficient anaerobic pathway). Rotor succeeds in this by flattening the power delivery curve, while the immovable ovals just phase-shift the curve.