Recent advances in short pulse lasers and time domain spectroscopies enabled investigation of molecular dynamics in a few femtosecond and even attosecond regime. Surprisingly however, time-dependent structural information is hard to come by. Vibrational spectra of molecules and materials recorded as a function of time may provide both dynamical and structural information. Vibrational spectra in electronic ground and excited states can be recorded by pump/probe transient absorption (TA) and time-resolved fluorescence (TF) through the impulsive excitation of vibrations, if they are recorded with a time resolution higher than the periods of vibrations of interest. The vibrational modes coherently excited by the pump pulses and their decay may provide a wealth of information on the dynamics and structures of the materials in a given electronic state. Theory on these time-domain spectroscopies including the selection rule and brief experimental techniques will be presented. Examples of applications of such studies including Franck-Condon transition, proton transfer, charge transfer, and internal conversion will be presented as well.