Wainscoting on stairs protects the walls from the usual scuffs of stairwell traffic. Its panels can be lozenge shaped and run smoothly up the side of the wall (as above, which I think is the more elegant option) or they can be stepped along with each stair tread.
Although I don't particularly like the colour combination in the picture below, it serves to show how well wainscoting and moulding can emphasis a curve:
A modern form of wainscot can be produced by applying moulding directly to the walls, creating a cameo effect:
For more on complete wall panelling and mahogany Wainscots see our post on The Study. For more on Gilded Boiserie work see our post on The Ballroom.