Abstract: Solution to the multiple scattering of electromagnetic (EM) waves by two arbitrary spheres has been pursued first by the multipole expansion method. Previous attempts at numerical solution have been thwarted by the complexity of the translational addition theorem. A new recursion relation is derived which reduces the computation effort by several orders of magnitude so that a quantitative analysis for spheres as large as 10\lambda in radius at a spacing as small as two spheres in contact becomes feasible. Simplification and approximation for various cases are also given. With the availability of exact solution, the usefulness of various approximate solutions can be determined quantitatively. For high frequencies, the ray-optical solution is given for two conducting spheres. In addition to the geometric and creeping wave rays pertaining to each sphere alone, there are rays that undergo multiple reflections, multiple creeps, and combinations of both, called the hybrid rays. Numerical results show that the ray-optical solution can be accurate for spheres as small as \lambda/4 in radius is some cases. Despite some shortcomings, this approach provides much physical insight into the multiple scattering phenomena.