How do you make curved folds in origami? I was Googling about, and saw some images of Dr. David Huffman's models and the work of the Demaines, and was curious how one makes curved freehand folds with any precision.  

So much of origami is taught as straight-line, corner-to-corner, or edge-to-edge straight folding. How do you make smooth, curved folds along predetermined lines?
Apart from just carefully folding along the curve with your fingers, following techniques get used:


Embossing the line with a pointed object or (better) a used-up ballpoint pen. Folding along such an embossed line results in a relatively smooth fold even if the curve is complex.
For some models (mostly the organic-looking ones), wet folding can allow very smooth lines to be folded. This is sometimes combined with scoring the paper using your fingernails. Daniel Chang uses such a technique for folding his realistic human faces.
Robert J. Lang famously uses a laser tool to score the crease pattern into the paper. I was able to fold from such paper in one of his workshops and the scored line looks a row of tiny perforations which weaken the paper and guide your hand when you fold along the line.
Some folders (e.g. Ekaterina Lukasheva) use digital plotter-like tools for embossing the paper.


Machine-embossed lines (the latter two examples) are of course much more precise than those made by hand, but even a line manually scored using a ball point pen can be surprisingly precise.