Magnetic nanostructures play a crucial role for the research in information technology, since magnetic materials are controllable on a nanometer scale. With decreasing size novel physical effects are observed which cannot be explained by means of theories describing macroscopic ferromagnets. In particular the understanding of the influence of finite temperatures on the reversal behavior and the magnetic stability of nanostructures is of broad interest since these aspects are very important for the development of new magnetic storage devices. This work gives an overview of numerical methods basing on a classical spin model. With the aid of these methods thermal activation processes can be investigated. The numerical solution of the Landau-Lifshtiz-Gilbert equation with Langevin dynamics as well as the Monte Carlo method with a so-called quantified time step is presented. This new procedure maps the quasi time scale of a Monte Carlo simulation on a realistic time scale. In this work activated magnetization processes in different kinds of nanostructures are investigated. Besides the investigation of fast switching processes, mainly the long-time behavior of elongated particles is studied. In these models different reversal mechanisms like coherent rotation, nucleation and curling can be observed depending on the sample geometry and the material parameters. In the one dimensional case, analytical asymptotic solutions for the energy barrier and the characteristic time exist, so that this model is convenient for testing the developed numerical methods. The implementation of the Fast Fourier Transformation method in the Monte Carlo method as well as the interpretation of the classical spin model in the sense of the continuums theory allows for a computer simulation of realistic systems. An application is the investigation of thermally activated reversal processes in nanowires during a hysteresis loop. The insights in the occurring reversal modes give information about the expected magnetoresistance. The results of these numerical investigations are compatible with the data from experimental observations of Conanowires.