Metamaterials are rationally designed composites with effective-medium properties that go beyond those of their ingredients. The talk gives an introduction into this field, which started around the year 2000 with negative refractive indices in optics. Examples given include sign inversion of the Hall coefficient, negative static compressibility, and nonlocal versions of Ohm's law as well as Hooke's law. Many of the underlying 3D microstructures have been realized by 3D laser nanoprinting.