Mie scattering is an important tool for diagnosing microparticles or aerosol particles in technical or natural environments. Mie theory is restricted to spherical, homogeneous, isotropic and non-magnetic particles in st non-absorbing medium. However, as microparticles are hardly ever spherical or homogeneous, there is much interest in more advanced scattering theories. During recent decades, scattering methods for non-spherical and non-homogeneous particles have been developed and even some computer codes are readily available. Extension of Mie theory covers coated spheres, stratified spheres and clustered spheres. For homogeneous non-spherical particles such as spheroids, ellipsoids and finite cylinders, surface discretization methods have been developed. Scattering by inhomogeneous particles may be computed by volume discretization methods.