Latest achievements in the theory of fast-light propagation in active Raman gain media are reviewed. Firstly, the linear propagation of light in three-level Λ-type and N-type active Raman gain media is introduced. Both of the systems are able to realize fast-light propagation with a negative group velocity. However, the N-type active Raman gain medium can exhibit a doublet structure in the gain spectrum based on the interference introduced by an additional coupling field. This feature can be used to effectively suppress the gain near the resonance. Secondly, the significant enhancement of Kerr nonlinearity in N-type active Raman gain medium is discussed. Thirdly, the nonlinear propagation of light in N-type active Raman gain media is introduced. Through a balance between the dispersion and nonlinearity of the system, it is possible to form a stable superluminal soliton at very low light level in such optically thick medium. A prospect is given in the end of the article.