Scientific and economic interest has recently turned to smaller and smaller magnetic structures which can be used in hard disk drives, magnetoresistive random access memory (MRAM), and other novel devices. For nanomagnets the geometric shape of the object becomes more important than other factors such as magnetocrystalline anisotropy . the smaller the object, the more strongly the shape anisotropy affects the hysteresis loop. We investigate the micromagnetic behaviour of ferromagnetic samples of various geometries using numerical methods. Finite differences and finite elements are used to solve the Landau-Lifshitz-Gilbert and Brown's equations in three dimensions. Simulations of basic geometric primitives such as cylinders and spheres of sub-micron size orders provide hysteresis loops of the average magnetisation, and additionally our computations allow the study of the microscopic configuration of the magnetisation. We show different mechanisms of vortex penetration for these geometries, and investigate part-spherical geometries whose magnetisation pattern demonstrates qualities of other primitives. Developing this further, we calculate the hysteresis loops for a droplet shape - a part-sphere capped with a half-ellipsoid. This resembles the shapes formed by some chemical self-assembly methods, a low-cost and efficient way of creating a commercially viable product. When examining the magnetic microstructure of this geometry we find different types of vortex behaviour, and reveal the dependence of this on the physical characteristics of the droplet. We also examine the hysteresis loops and magnetic structures of other geometries formed through the self-assembly method such as antidots:honeycomb-like arrays of spherical holes in a thin film. We show magnetisation patterns and comparison between experimental and computed magnetic force microscopy (MFM) measurements.