In the past decade, a revolution in materials sciences has been brought about by the recognition of topology in characterizing the physical properties. These materials which support nontrivial topological phases are termed as topological materials. The related research is now beyond the electric system and the phenomena have been realized in other systems such as photonics, acoustics and mechanics. In this talk, I will introduce some results on these materials from the applied analysis and numerics aspects. Especially, I will focus on photonic topological materials, including existence of Dirac points, topological edge states and topologically protected wave motions and corresponding numerical methods.