The vibrational dynamics of polyatomic solutes in polyatomic liquid and glassy solvents are examined using picosecond infrared photon echo experiments and pump-probe experiments from room temperature to 10 K. The photon echo experiments measure T-2, the homogeneous dephasing time (homogeneous line shape), while the pump-probe experiments measure the vibrational lifetime, T-1, and the orientational relaxation dynamics. By combining these measurements, a complete analysis of vibrational dynamics is obtained in the liquid, in the supercooled liquid, through the glass transition, and in the glass. Experiments were conducted on the asymmetric CO stretching mode of tungsten hexacarbonyl (similar to 1980 cm(-1)) in 2-methylpentane (2-MP), 2-methyltetrahydrofuran, dibutyl phthalate (DSP), carbon tetrachloride, and chloroform. The experiments were conducted using the picosecond IR pulses from a superconducting-accelerator-pumped free electron laser. The absorption line widths for all glasses are massively inhomogeneously broadened at low temperature. In the room temperature liquids, while the vibrational line in 2-MP is homogeneously broadened, the line in DBP is still extensively inhomogeneously broadened. The temperature dependences of the homogeneous line widths in the three glasses area T-2 power law. The contributions of vibrational pure dephasing, orientational relaxation, and population lifetime to the homogeneous line shape are examined in detail in the 2-MP solvent. The complete temperature dependence of each of the contributions is determined. In addition; the temperature dependence of T-1 is observed to be "inverted" in most of the solvents; i.e., the lifetime becomes longer as the temperature is increased. Analysis shows that this is caused by temperature dependence of the anharmonic coupling matrix elements.