While the formation and growth of soot particles has received much attention, the subsequent destruction of the particles is less well understood. Soot particles are destroyed through two parallel processes: oxidation and fragmentation. Oxidation is the removal of mass from particles due to chemical reactions with molecular oxygen and hydroxyl radicals. Fragmentation is the break-up of large aggregates into smaller aggregates. Models for both oxidation and fragmentation are presented. To statistically describe the population, the two models are implemented in both Monte Carlo (MC) simulations and the Hybrid Method of Moments (HMOM). In the implementations, particles are described with Volume and Surface area (VS) to account for the presence of fractal aggregates. The models are validated in a set of laminar premixed methane flames and allow the simultaneous prediction of total soot mass, total soot number density, and average particle size. Additional models needed for unclosed terms in HMOM are also developed and discussed.