In this dissertation we study the behavior of several computational models of a magnetic nanopillar. We first compare the effect that coarse-graining the computational lattice has on the magnetization switching for three degrees of discretization. Bimodal switching-time distributions are found for all three models, however the underlying mechanism is different for each one. In the lowest-resolution, single-spin model, a bimodal distribution is the result of spin precession which sometimes crosses the threshold defining a switching event early or in the next precession period, depending on thermal fluctuations. For the medium-resolution, stack-of-spins model, the presence of either one or two propagating domain walls during the switching event determines the total switching time, leading to the observed bimodal distribution. The most realistic model, which employs a high-resolution computational lattice, permits multiple switching paths, some of which are characterized by their visitation to a metastable free-energy well and consequently longer lifetimes. It is also notable that the medium-resolution model exhibits reentrant behavior for reversal fields that are applied close to the easy axis. The highest-resolution model is studied in detail, due to its complexity, which precludes a simple description of the mechanism resulting in bimodal switching-time behavior. Phase-space portraits of components of the total energy indicate that the metastable free-energy basin is circumvented for short-lived trials. Sufficient statistics are gathered to allow Markov matrices describing the average behavior of each mode to be investigated. Eigenvectors of these matrices provide estimates of the probability distribution of the largest transient for each mode in the energy space, while the projective dynamics technique identifies the location of the free-energy saddle point. The hypothesis that the visitation of the metastable well underlies the bimodal behavior is further reinforced by comparing the long-lived trials to simulations that are constrained to start in the metastable state. Finally, exploratory results for thermally-assisted magnetization reversal of the highest-resolution model are provided to test the assumption that it is only necessary to increase the temperature at the endcaps of the pillar, since this the site of nucleation. By introducing additional thermal energy to the pillar, the coercive field might be lowered, relaxing the required field of the write head of a hard disk drive. We find that varying the maximum temperature of a narrow pulse, centered at the top of the pillar, results in a very modest change in the coercivity when the maximum temperature is kept close to, or below, the Curie temperature. This effect is largely limited by the added heat diffusing quickly to the constant-temperature substrate. Switching fields were significantly reduced for pulse widths that were large enough to elevate the temperature of the entire pillar. However, using such large pulses stretch the approximations of the model. Another approach is attempted, tuning the parameter that controls energy exchange between the temperature bath and the spins. This also results in only a minimal reduction of the coercive field. Some suggestions are given for future computational studies of thermally-assisted magnetization reversal.