||In this thesis, we developed a boundary element method (BEM) for electromagnetic computations. We accelerated the BEM using fast multipole method (FMM), which makes our method qualified for large scale computations. Using the method developed, we studied two interesting optical problems. In the first one, we proposed a method to achieve exterior optical cloaking/illusion effects using active sources (a set of monopoles and dipoles placed on continuous curves). These active sources create a nearly 'silent' domain which can conceal any objects inside and at the same time generate out going waves mimic those scattered by another object of our choice. By such, we can optically transform an apple to an banana. In the second problem, we examined the image formation of objects placed in front of a metamaterial slab and discovered a fundamental phenomenon: a metamaterial slab (with arbitrary ε and μ) will suppress the optical excitation of the objects placed sufficiently closed to it, and make the object invisible. We found that this universal suppression/cloaking effect is due to the enhanced evanescent reflection. This enhanced reflection is extremely strong in perfect lens systems (including the Veselago slab and other unfolding geometry slabs, so that they can cloak objects at a finite distance (d/2, d is the slab thickness), i.e., all the objects lie within a distance d/2 to the slab will be completely cloaked.