Two methods for computing the (asymptotic) electromagnetic scattering by arbitrarily-shaped targets are described: the Eikonal model, valid for objects whose overall size is much greater than the incident wavelength (based on a quantum partial-wave expansion in the scalar approximation); and the low-energy model, valid for objects whose overall size is comparable to the incident wavelength (based on a discretization of the scattering object). Their numerical results are compared to those of exact theories in the cases of perfect spheres and spheroids. Comparisons to experimental data for irregular objects (Eikonal model) and dielectric helices (low-energy model) are described, as well as theoretical predictions for rough scatterers.>