Raman spectroscopy is broadly used in the studies of 2-dimensional layered materials to determine the number of layers or other physical properties. In the case of graphene, the line shape and the position of the 2D band depend on the excitation energy due to the inter-valley double resonance scattering and can be used to determine the number of layers and the stacking order. In the case of transition metal dichalcogenides (TMD’s), the Raman spectrum varies greatly depending on the excitation energy, and many interesting effects have been reported. The Raman intensities of high-frequency intra-layer vibration modes are enhanced near resonance with exciton states, and due to the strong excitonic resonance effects, some Raman peaks that are either forbidden or weak in non-resonant cases show strong enhancement near resonances. Ultralow-frequency Raman spectra below 50 cm^–1 reveal details of the weak van der Waals interaction between the layers. They can be used to determine the number of layers and the polytypes (stacking order) accurately. Some intra-layer vibration modes exhibit Davydov splitting due to the weak inter-layer interactions when the excitation energy is close to resonances. Recently, Raman spectroscopy is playing an important role in the studies of a new class of 2-dimensional magnetic materials. In this seminar, I will review some important examples of the use of Raman spectroscopy in 2-dimensional materials research.