The unsteady hydrodynamics of tidal stream turbines have been investigated using numerical methods and experiments. Dynamic inflow, which represents the change in backflow induced by the circulation present in the wake due to variations in rotor loading, is the particular focus of this work. An implementation of an unsteady vortex lattice method has been developed for modelling tidal stream turbines in a variety of flow conditions. The vortex lattice method is an inviscid potential flow solver, with the blades represented as surfaces on the camber line. The vortex lattice method is used to analyse the difference between a sudden collective change in blade pitch, compared with a sudden change in mean flow. The observed differences are explained with the examination of several simulation properties, such as the wake induced flow field. The vortex lattice method is also used to model a tidal turbine in an oscillatory flow environment. Additionally, experiments have been conducted in a recirculating water flume. A scale turbine model is mounted on a controllable carriage, which can move arbitrarily along the flow direction. Strain gauges are place at the root of one turbine blade, and on the mounting strut of the turbine. This thesis examines the loading response of the turbine due to oscillation of the carriage and turbine system, over a range of Keulegan-Carpenter numbers and current numbers. The conclusions drawn from the experimental and numerical work describe the degree of importance of dynamic inflow, and will show that it can be responsible for overshoots in turbine thrust loads, and lag in the load response when the turbine is subjected to oscillating flow. Dynamic inflow is shown to have significant influence on the turbine thrust in unsteady flows. Added mass, the inertial force that arises when accelerating a body through a fluid is also investigated with two-dimensional unsteady airfoil theory, and is estimated to have an important role in the unsteady loading of tidal stream turbines. A two-bladed device is the main point of interest in this thesis, however the concepts can be extended for many rotor designs.