Classically, studies of the water wave problem focus on the shallow water limit. Famous examples of such studies include the seminal works by Stokes (1847) and Korteweg and de-Vries (1895). In this talk I will discuss how the mathematical properties of the water wave problem change when surface tension is included – in deep water. Recent analogues of these famous studies will be presented – including a modern method for computing periodic waves and a simple model for the dynamics of gravity-capillary solitary waves.