  The ropelength of a knot is the quotient of its length and its thickness, the
radius of the largest embedded normal tube around the knot. We prove existence
and regularity for ropelength minimizers in any knot or link type; these are
$C^{1,1}$ curves, but need not be smoother. We improve the lower bound for the
ropelength of a nontrivial knot, and establish new ropelength bounds for small
knots and links, including some which are sharp.
