We discuss the numerical solution of the 3-D Maxwell's equations in general curvilinear coordinates using a multidomain pseudospectral (Chebyshev collocation) scheme. The formulation of the equations and the method as well as the multidomain patching procedure is reviewed. We also discussed the modeling of various materials. Very accurate numerical results are obtained when simulating scattering by perfect electrically conducting (PEC), dielectric, and lossy dielectric objects such as a cube, a sphere, and a cylinder. The use of spectral methods, especially multidomain spectral methods, appears to be very promising for accurately simulating electromagnetic wave problems. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.