We examine different models and methods for studying finite-tempera-ture magnetic hysteresis in nanoparticles and ultrathin films. This includes micromagnetic results for the hysteresis of a single magnetic nanoparticle which is misaligned with respect to the magnetic field. We present results from both a representation of the particle as a one-dimensional array of magnetic rotors, and from full micromagnetic simulations. The results are compared with the Stoner-Wohlfarth model. Results of kinetic Monte Carlo simulations of ultrathin films are also presented. In addition, we discuss other topics of current interest in the modeling of magnetic hysteresis in nanostructures, including kinetic Monte Carlo simulations of dynamic phase transitions and First-Order Reversal Curves.