This thesis presents advancements in the understanding of the plasma conditions leading to the excitation and saturation of the Edge Harmonic Oscillations (EHOs) observed during QH-mode operation in tokamak plasmas. Such operations represent a safer alternative with respect to H-mode due to the absence of Edge Localised Modes (ELMs) while retaining high energy confinement and pedestal height. In this work, EHOs have been assumed to be the nonlinear evolution of linearly unstable external infernal (exfernal) modes. It is consistently found that exfernal modes can be excited and nonlinearly saturated in wide regions of the parameter space. Such regions have been identified through the use of various analytical and numerical tools developed within the ideal MHD model, including linear analytical modelling, linear stability software, and nonlinear equilibrium and initial value simulations. An expanded set of large aspect ratio equations describing the linear stability of exfernal modes is derived analytically, including higher order terms in the expansion of the safety factor around the rational surface, which allows for the effects of finite edge magnetic shear. Numerical solution of the equations provides the linearly unstable exfernal mode parameter space with respect to pedestal pressure gradient, pedestal width, edge safety factor and edge magnetic shear. Nonlinearly saturated exfernal modes calculated with the 3D VMEC free boundary code are found in regions of the parameter space where the exfernal modes are linearly unstable to the 2D VMEC neighbour state. The obtained critical value of the edge magnetic shear in the VMEC simulations is also recovered by the linear stability analysis. The parameter space is found to be reduced by the presence of a plasma separatrix due to a partial stabilisation of the external kink current-driven branch of the exfernal mode. An analytical estimation of the critical magnetic shear for the excitation of exfernal modes in diverted plasmas is also presented. Finally, it is shown that the parameter space for the saturation of external modes can be expanded through the application of non-axisymmetric Magnetic Perturbations (MPs). This is done analytically using a linear time-invariant perturbation of the 2D equilibrium assuming an external helical magnetic perturbation, and also in the VMEC code by the inclusion of non-axisymmetric coils in the calculation of the vacuum field. The approaches were applied to saturated external kink and exfernal modes. For the external kink case, quantitative agreement is found in the saturated amplitude obtained with the linear model and with the VMEC code for cases where the external kink is stable in the absence of MPs. For the case of saturated exfernal modes, only qualitative agreement is found, possibly due to the approximations taken in the calculation of the analytical model. Nevertheless, a significant expansion of the parameter space of saturated exfernal modes is obtained via the introduction of symmetry breaking coils, resulting in an appealing route for future reactor operations.