Theoretical understanding of photoinduced phase transitions and their dynamics is reviewed from the viewpoint of coherent oscillations and transient states in condensed molecular materials with quasi-one-dimensional electronic conduction. In the mixed-stack organic charge-transfer compound TTF-CA (TTF: tetrathiafulvalene, CA: chloranil), the photoinduced transition from the ionic phase to the neutral phase is accompanied with coherent motion of a neutral-ionic domain boundary. Its high cooperativity is realized by the sufficiently strong, interchain Coulomb coupling in the ionic phase. In the quarter-filled-band organic salt (EDO-TTF) 2PF6 (EDO: ethylenedioxy), the photoinduced melting of charge order is accompanied with oscillations in transient reflectivity. The degree of coherence in these oscillations depends on the probe photon energy. It is caused by different space and time scales of observed electronic motion and relevant phonon motion.