The ability of a liquid to wet a solid substrate is determined by the chemistry and physical texturing of the surface. At the two theoretical extremes, a liquid drop on a surface can completely spread to a film or bead to a perfect sphere. In practice, some form of intermediate or partial wetting is obtained with the liquid adopting a spherical cap shape. Two metrics are commonly employed to specify the surface wettability: rest or static contact angle (_) and contact angle hysteresis (__). Partially non-wettable surfaces are characterized by static contact angles _ > 90° while partially wettable surfaces _ < 90°. Contact angle hysteresis, defined as the difference in dynamic advancing and receding contact angles, specifies contact line stick-slip behavior with higher hysteresis corresponding to a greater extent of contact line pinning. Understanding how liquids wet and dynamically behave on solid surfaces has widespread importance in application areas ranging from natural to industrial to technological. As such, it has historically attracted much scientific attention. This dissertation studies how surface wettability influences drop behaviors in the interrelated areas of coalescence, condensation heat transfer, and inertial-capillary (rapid) spreading. In the first part of this dissertation, experiments and numerical simulations are employed to examine how changing the surface wettability, via modification of _ & __, influences sweeping during sessile drop coalescence. Coalescence sweeping results from the dynamic shape reconfiguration associated with the drop merging process and has relevance to self-cleaning, anti-frost, condensation, and water harvesting applications. In the second part of this dissertation, a surface with switchable superhydrophilic to hydrophobic wetting behavior is developed that responds to temperature stimulus. This surface is successfully applied as a condenser that exhibits variable performance in its heat transfer coefficient by switching between the filmwise and dropwise modes of condensation, with ultimate relevance to space-based thermal management applications. Theory is also applied to understand how surface wettability affects fundamental drop processes during dropwise condensation, and to elucidate dropwise to filmwise condensation transitions. Finally, in the third part of this dissertation, a contact line mobility parameter is hypothesized as a means to understand and predict liquid spreading in situations where inertia and capillarity compete. Drop vibration experiments will be performed on the International Space Station (ISS) in 2020 to measure the mobility parameter, and subsequent drop-drop coalescence experiments will examine the utility of the mobility parameter as a predictive tool. ISS microgravity manifests a magnified capillary length scale which transforms the inertial-capillary spreading problem from a small and fast event on Earth to one that is larger and slower in space thereby enabling easier characterization. Preliminary results are reported for an analogous ground-based study that assesses the validity of mobility parameter utilization for predictive application.