In this paper, the finite-difference time-domain ({FDTD}), multiple-region/{FDTD} ({MR/FDTD}) and ray-tracing/{FDTD} ({RT/FDTD}) techniques have been compared with reference to the study of the field scattered by and induced inside an exposed target. The three techniques have been validated on a free-space radiation problem through a comparison with the MoM solution. Compression techniques have been implemented to obtain a reduction of the computational costs associated with {MR/FDTD}, performing an accurate evaluation of the associated errors. The applicability and accuracy of the three techniques have then been tested studying the exposure of a sphere to a half-wavelength dipole. The obtained results have shown that the best computational performances are achieved employing {RT/FDTD}. However, this technique gives accurate results only in the radiative far-field of the antenna. {MR/FDTD}, instead, gives accurate predictions of field distributions for a wide range of distances between the scatterer and the antenna and, thanks to the introduction of compression techniques, requires acceptable computational costs. Pure {FDTD}, finally, is the most suitable technique, among the three considered, when the scatterer is close to the antenna but its computational costs become prohibitive for large-scale problems.