The author surveys the areas of knot theory relating to quasipositivity, the enhanced Milnor number and the (perhaps still) new link polynomials. While singularities of plane algebraic curves are central to the survey, many other things are discussed. Along with the results, a number of conjectures and problems are presented. Some of the theorems and corollaries are proved, and many (but not all) of the requisite definitions (and some pictures) are provided to assist in understanding the material. In addition many helpful suggestions as to ways of thinking about results are given.