Wetting and spreading are ubiquitous surface phenomena which occur when a liquid is brought into contact with a solid surface. They are part of Nature's toolbox in the functional adaptation of many biological systems and we often make use of them in our technological processes. \Vetting is driven by surface forces, the so-called surface tensions, and it becomes increasingly important as the typical region occupied by the liquid becomes smaller. As miniaturisation of fluidic operations lead to surface structures on the micron and nanoscale, wetting phenomena become very rich, partly because the length scale of the surface heterogeneities is now comparable to the size of the system. This is the focal point of this thesis. \Ve arc interested in how micron-scale surface patterning can alter the wettability of the surface. Two types of patterning are addressed in the thesis, chemical and topological. Both patternings lead to complex drop morphologies that depend sensitively on the parameters of the patterns, as well as the path by which the system is prepared. The contact angle of the drop is no longer uniquely determined, leading to a phenomenon called contact angle hysteresis, and the drop shape may differ considerably from a spherical cap. This anisotropy can, in return, be exploited for microfluidic operations. \Ve show how appropriate patterns may be used to control drop size and polydispersity, as well as to enhance or slow down capillary filling. Topological patterning may also lead to superhydrophobic behaviour. This can occur in two diH'erent ways. \Vhen a liquid drop is placed on a superhydrophobic surface, it can either be suspended on top of the corrugations or fill the space in between the posts. \Ve discuss in particular how the apparent contact angle and the contact angle hysteresis are affected by the surface roughness in these two states, and investigate when a transition may occur from the suspended to the collapsed state as the drop evaporates. Analytical descriptions of drop morphologies are often not possible and nUlnerical modelling is needed. This is done using a mesoscale modelling technique called the lattice Boltzmann method. \Ve present three models which may be used to model wetting phenomena: the liquid gas, the binary, and the binary liquid gas model and discuss the relative strengths and weaknesses of each approach.