The most important device for today's large scale information storage is the magnetic hard disk drive. This is because it can store vast amounts of data and also provides the fastest way of accessing this valuable information. A current state of the art commercially available hard disk has data rates in excess of 1 GHz which means the magnetic bits are required to reverse in less than one nanosecond. The areal density is greater than 10 Gbits/in2 which requires extremely small magnetic grains with sizes of approximately 10 nm. These are so small that their magnetisation can be affected by the ambient thermal energy and in extreme cases the information can be lost. It is imperative, for our rapidly growing system requirements, that we characterise and understand the mechanisms of thermally activated high frequency magnetisation dynamics, and that is the main aim of this thesis. Our approach is based upon the numerical solution of the Langevin equation of the problem. The solution of this stochastic differential equation is carried out by using Stratonovich stochastic calculus methods which generates the fluctuating trajectories of the individual magnetic moments. The model was first applied to the study of thermal relaxation and computed results showed non-exponential relaxation over small energy barriers. The coercivity was seen to rapidly increase for very high frequency field pulses which is important as regards to the ultimate switching speeds in recording. The short time scale breakdown of the Arrhenius-Neel law for a single magnetic moment is demonstrated and explained in terms of the dynamics of the precess ional motion. The variation in response as a function of the damping parameter is found to be an important factor determining the remanent magnetisation for a given pulse width. The effects of interactions between moments are described, including the apparent increase in effective damping. It is shown that interactions between grains can be described in terms of thermally excited spin waves.