Linear Water Wave theory is one of the most important branches on fluid mechanics. Practically it underpins most of the engineering design of ships, offshore structures, etc. It also has a very rich history in the development of applied mathematics. In this talk I will focus on the connection between solutions in the frequency and time-domains and show how we can use various formulations to make numerical calculations and to construct approximate solutions. I will illustrate these methods with application to some simple wave scattering problems.