Floating offshore wind turbines are subjected to large motions due to the additional degrees of freedom of the floating foundation. The turbine rotor often operates in highly dynamic inflow conditions, and this has a significant effect on the overall aerodynamic response and turbine wake. Experiments are needed to get a deeper understanding of unsteady aerodynamics and hence leverage this knowledge to develop better models and to produce data for the validation and calibration of existing numerical tools. In this context, this paper presents a wind tunnel experiment about the unsteady aerodynamics of a floating turbine subjected to surge motion. The experiment results cover blade forces, rotor-integral forces, and wake. The 2D sectional model tests were carried out to characterize the aerodynamic coefficients of a low-Reynolds-number airfoil with harmonic variation in the angle of attack. The lift coefficient shows a hysteresis cycle close to stall, which grows in strength and extends in the linear region for motion frequencies higher than those typical of surge motion. Knowledge about the airfoil aerodynamic response was utilized to define the wind and surge motion conditions of the full-turbine experiment. The global aerodynamic turbine response is evaluated from rotor-thrust force measurements, because thrust influences the along-wind response of the floating turbine. It is found that experimental data follow predictions of quasi-steady theory for reduced frequency up to 0.5 reasonably well. For higher surge motion frequencies, unsteady effects may be present. The turbine near wake was investigated by means of hot-wire measurements. The wake energy is increased at the surge frequency, and the increment is proportional to the maximum surge velocity. A spatial analysis shows the wake energy increment corresponds with the blade tip. Particle image velocimetry (PIV) was utilized to visualize the blade-tip vortex, and it is observed that the vortex travel speed is modified in the presence of surge motion.