For plane curve singularities most questions have been answered, in large part due to the Newton-Puiseux expansion. I've heard that there are a number of open problems regarding space curve singularities but have not found any clear statements. (One problem or set of problems seems to be around the characterization of which semigroups can arise.) Could someone point me to some of these problems? I am primarily interested in local singularities, over the complex numbers or reals, and to start with, unibranched singularities.