In this chapter, we overview double resonance Raman spectra of two dimensional materials. Many weak Raman spectral peaks are observed in the two dimensional materials which can be attributed to second order, double resonance Raman spectra. It is useful for material characterization to understand not only first order Raman spectra but also second order Raman spectra since the second order Raman spectra has more information on electronic structure of the materials than the first order Raman spectra. Combined with the conventional first order resonance Raman theory, we will explain why the double resonance condition can be strong in the two dimensional materials. Since the double resonance Raman spectra give the information of phonon with non-zero wavevectors in the Brillouin zone, both the resonant wavevector and corresponding Raman spectra can shift with changing the incident laser energy. Here we will discuss the physics of double resonance Raman spectra of graphene, transition metal dichalcogenides by theoretical analysis using the first principles calculation.