Usually, investigators in materials science have asked: “What properties does a certain new material or structure have?” Now, the inverse problem arises: “I want to achieve certain—possibly unheard-of—material properties. How should the corresponding micro- or nanostructure look?” Examples could be: efficiently blocking acoustic noise due to a highway from a nearby village by a tailored wall, concentrating electromagnetic energy into as-tight-as-possible spaces, or avoiding reflections from a material's surface. The underlying common scheme is wave physics. Material properties that were otherwise unachievable, e.g., negative refraction and cloaking, may eventually be designed into optical metamaterials and photonic crystals. Both require tailoring of the properties (i.e., phase velocity and impedance) of an electromagnetic wave moving through the substance at the local level. In photonic crystals, the phase velocity of an electromagnetic wave moving through the crystal is controlled by tuning the photonic band structure; the impedance is determined by the electromagnetic field distributions throughout the material. In metamaterials, this amounts to tailoring the effective electric permittivity and magnetic permeability. In either case, introducing resonances is the key to controlling the local wave properties. The recent development of advanced fabrication techniques being applied to metamaterials and photonic crystals may lead to realization of such designer materials.