The leptonic mixing matrix may be understood as a consequence of remnant symmetries of the mass matrices, which emerge from the spontaneous breakdown of a larger symmetry into smaller non-commuting subgroups. The mixing patterns that may be obtained from groups of order smaller than 1556 are presented. To dynamically realize this symmetry breaking pattern an additional mechanism is needed. Here a minimal solution to this problem is provided, based on non-trivial extensions of the flavour group. A scan over possible extensions of popular flavour groups is presented and the smallest semidirect product extension of the group A4 is discussed. A model based on this symmetry group is constructed and it is shown to naturally give the required vacuum structure. Modifications that can account for the deviation from the predicted value for the mixing angle θ13 are presented. The vacuum alignment mechanism is applied in a model at the electroweak scale, which contains a dark matter candidate, and its phenomenology is studied. Consistency conditions for CP transformations in the context of discrete flavour groups are developed and they are shown to have non-trivial implications for existing models. Finally, we give an outlook about how the Standard Model may be viewed from a Planck scale perspective.