In this study, large eddy simulation (LES) is combined with a turbine model to investigate the wake behind a vertical-axis wind turbine (VAWT) in a three-dimensional turbulent flow. Two methods are used to model the subgrid-scale (SGS) stresses: (a) the Smagorinsky model; and (b) the modulated gradient model. To parameterize the effects of the VAWT on the flow, two VAWT models are developed: (a) the actuator swept-surface model (ASSM), in which the time-averaged turbine-induced forces are distributed on a surface swept by the turbine blades, i.e., the actuator swept surface; and (b) the actuator line model (ALM), in which the instantaneous blade forces are only spatially distributed on lines representing the blades, i.e., the actuator lines. This is the first time that LES has been applied and validated for the simulation of VAWT wakes by using either the ASSM or the ALM techniques. In both models, blade-element theory is used to calculate the lift and drag forces on the blades. The results are compared with flow measurements in the wake of a model straight-bladed VAWT, carried out in the Institute de Mechanique et Statistique de la Turbulence (IMST) water channel. Different combinations of SGS models with VAWT models are studied, and a fairly good overall agreement between simulation results and measurement data is observed. In general, the ALM is found to better capture the unsteady-periodic nature of the wake and shows a better agreement with the experimental data compared with the ASSM. The modulated gradient model is also found to be a more reliable SGS stress modeling technique, compared with the Smagorinsky model, and it yields reasonable predictions of the mean flow and turbulence characteristics of a VAWT wake using its theoretically-determined model coefficient.