Magnetic nanoparticles are useful biological probes as well as therapeutic agents. Several approaches have been used to model nanoparticle magnetization dynamics for both Brownian as well as Neel rotation. Magnetizations are often of interest and can be compared with experimental results. Here we summarize these approaches, including the Stoner-Wohlfarth approach and stochastic approaches including thermal fluctuations. Non-equilibrium-related temperature effects can be described by a distribution function approach (Fokker-Planck equation) or a stochastic differential equation (Langevin equation). Approximate models in several regimes can be derived from these general approaches to simplify implementation.