The basic mathematical phenomena relevant to ocular damage caused by ultrashort laser pulses are discussed with the use of mathematical results and numerical modeling. The primary effects of nonlinear self-focusing and beam collapse are examined in the ocular safety context. Finite-time material response and group-velocity dispersion are discussed as possible mitigating factors. An argument is presented that indicates that the initial stages of beam collapse are essentially two-dimensional. Experiments are suggested that might help distinguish the most important contributing factors in the damage regime. The numerical methodology is detailed in an appendix.