Acenes and perylene dyes have been a focus of fundamental research for decades, motivated partly by applications in organic photovoltaics and light-emitting diodes. The lowest triplet excited state of these molecules is of interest, because these transient species are closely associated with loss processes as well as mechanisms for new applications (e.g. singlet fission, or triplet-triplet annihilation). Vibrational spectroscopy of molecules in the T1 state is motivated because this approach provides structural insights, and is generally more specific than other techniques such as electronic spectroscopy. This work focuses on resonance Raman spectroscopy, because this technique greatly amplifies the signal from specific targets.The first part of this dissertation describes resonance Raman spectroscopy of the ground (S0), excited triplet (T1), and cationic states of pentacene (Pn) as well as a soluble derivative (triisopropylsilylethynyl-pentacene, TIPS-Pn). Unique signatures were found for each state. These spectra serve as a useful reference for Pn and its derivatives, in solution or solid state. Density functional theory computations that account for resonance enhancement were used to assign bands to specific vibrational normal modes. Shifts in the frequencies, some exceeding 30 cm-1, were analyzed in terms of local mode character, and frontier molecular orbitals. The second part of this dissertation describes a resonance Raman study of a representative perylene diimide molecule in its lowest triplet excited-state (3PDI*). The PDI family is one of the most important synthetic dyes, yet the vibrational structures of their excited states are not well characterized. One obstacle is that high fluorescence from PDI, with quantum yields typically near 100%, overwhelm signals from Raman scattering. To overcome this problem, two cofacial PDI dimers were synthesized, both with fluorescence emission reduced by a factor of ~100. Improvements to a two-chamber pressurized flow system permitted rigorous exclusion of oxygen and allowed many hours of data acquisition. The vibrational spectra of the S0 and T1 states are readily distinguished, and the bands in the range 500 -1700 cm-1 are analyzed as described above for pentacene. As a whole, this works extends the use of resonance Raman spectroscopy and accompanying computations with resonance as useful tools for identifying and probing the triplet excited states.