Basically red shift means that frequency of phonons interacting with the incident photon decreased, blue shift means that it increased. Reasons?
1. Heating. Expanding of material leads to frequency decrease. Red shift.
2. Strain. If the material lattice is compressed the Raman shift increases, if it is under tensile strain - decreases.
3. Other structural changes in the material (e.g. chemical interaction). Solid solution (AlGaAs) will have frequencies different from pure materials (AlAs and GaAs). As for organic materials, there effect of chemical bonds is not easy to predict but will still occur.
4. Other effects like phonon confinement.