Femtosecond broadband stimulated Raman spectroscopy (FSRS) is a new technique that produces high-resolution (time-resolved) vibrational spectra from either the ground or excited electronic states of molecules, free from background fluorescence. FSRS uses simultaneously a narrow bandwidth similar to1-3 ps Raman pump pulse with a continuum similar to30-50 fs Stokes probe pulse to produce sharp Raman gains, at positions corresponding to vibrational transitions in the sample, riding on top of the continuum Stokes probe spectrum. When FSRS is preceded by a femtosecond actinic pump pulse that initiates the photochemistry of interest, time-resolved Raman spectroscopy can be carried out. We present two theoretical approaches to FSRS: one is based on a coupling of Raman pump and probe light waves with the vibrations in the medium, and another is a quantum-mechanical description. The latter approach is used to discuss the conditions of applicability and limitations of the coupled-wave description. Extension of the quantum-mechanical description to the case where the Raman pump beam is on resonance with an excited electronic state, as well as when FSRS is used to probe a nonstationary vibrational wave packet prepared by an actinic pump pulse, is also discussed. (C) 2004 American Institute of Physics.