The behaviour of waves on the surface of a fluid has fascinated scientists for centuries. Attempts to describe the problem mathematically have revealed a rich geometric structure, as well as a number of celebrated equations. When considering a stochastic theory of water waves, it is therefore sensible to begin with a structure preserving methodology of introducing a stochastic noise into a fluid model. Within this thesis, the mathematical framework of semi-martingale driven variational principles is introduced, which reveals a new methodology of formulating problems for which we have a stochastic action integral. The inclusion of stochastic advection by Lie transport into the underlying fluid momentum equation will allow us to achieve a novel stochastic perturbation of water wave theory which preserves its geometric properties. A number of phenomena observable on the free surface of a fluid are challenging to describe using existing modelling approaches. In particular, the classical modelling approach requires modification to permit the introduction of thermal gradients or rotational flows. Through a new variational perspective involving the composition of two maps, the interaction between waves and thermal fronts in the upper ocean is studied. This approach involves a natural separation of waves and currents on the free surface as vertical oscillations around a horizontal two dimensional flow, and allows the consideration of wave-current interactions. Separately, currents are responsible for the advection of material suspended within the fluid. We consider the procession of an inertial object through a fluid domain, which involves fluid equations with the structure of a fractional order differential equation. It is shown that the most commonly applied such equation, the Maxey-Riley equation, is globally well-posed, a fact which was absent from the literature prior to this thesis.