Many experiments have been carried out to determine the relative strengths of different knots in fibers and ropes, and these show that the break in a knotted rope almost invariably occurs at the point just outside the "entrance" to the knot. The influence of knots on the properties of polymers is of continuing interest, in part because of their effect on mechanical properties. Knot theory applied to the topology of macromolecules indicates that the simple trefoil or "overhand" knot is likely to be present in any long polymer strand. Fragments of DNA have been observed to contain such knots in both experiments and computer simulations. I will review the salient parts of the history of knots in polymers, including ab initio computational studies used to investigate the effect of a trefoil knot on the breaking strength of a polymer strand. New computational studies on various knots in polyethylene will be reported. These new computational studies have employed so-called neural network potentials (NNPs) fitted to high level electronic structure calculations on hydrocarbons with single, double and triple bonds, radicals, and bulk structures. The new computations confirm that knots weaken a polymer strand significantly, and like in a macroscopic knotted rope, usually break under tension at the entrance to a loop in the knot.