This Thesis addresses the thermodynamic behaviour of two-dimensional mag nets. The objective is to evaluate the role played by external perturbations in these systems by use of analytical and computational techniques. To this end, extensive Monte Carlo simulations have been performed on Ising, XY and Heisenberg spin models in the presence of symmetry breaking crystal fields, external magnetic fields and long range dipolar interactions. The effects of four-fold symmetry are examined in detail, since this is common in nature. In the 2dXY model, such a crystal field acts as a marginal perturbation which drives the system to non-universal critical behaviour only upon reseating to exponentially large length scales. This has the implication that real, finite systems are unexpectedly robust to their presence. On the other hand, the four-state clock model is recovered in the limit of extremely strong fields, which exhibits Ising critical behaviour. The nature of this crossover from XY to Ising behaviour is studied in detail, using numerical and analytical methods. The picture that emerges from this analysis is that there are two principal categories of two-dimensional magnets: those belonging to the so-called Ising uni versality class and those belonging to the XY class. A detailed survey of the experimental literature confirms this classification. However, a considerable num ber of experimental systems also exhibit behaviour wrhich is intermediate between these two regimes. It is argued these materials are susceptible to the crossover mechanism induced by the presence of four-fold fields.