Vibrational spectra are frequently used for studies of the structure and dynamics of peptides and proteins. Structural interpretation of the experimental data, however, requires theoretical simulation of the spectra for model peptide geometries. Quantum mechanical, in particular density functional theory (DFT), methods have proven exceptionally valuable for calculations of the vibrational force fields and both IR and Raman intensities. A brief review of some recent trends in computation of molecular force fields and spectral intensities is presented. Particular attention is paid to experiments involving circularly polarized light, as these provide enhanced structural information for chiral molecules. Following a historical overview of common approaches, the fundamental theoretical aspects of the calculations of the molecular vibrational spectra are summarized. Special emphasis is given to the problem of simulating spectra for biological molecules (oligo-peptides and nucleotides, proteins and nucleic acids) using DFT methods. The methodology for simulations of large biopolymers with DFT level force fields and intensity parameters abstracted from smaller molecules is reviewed. Several examples with the discussion of successes and difficulties of the vibrational spectra simulations for model peptides are presented. Finally, methods for incorporating the solvent in the spectral simulations are reviewed and discussed.