The phenomenology of impulse-regime propagation along metamaterial composite right/left-handed transmission lines (CRLH TL) is examined. For this purpose, a closed-form time-domain Green's function approach, based on the inverse Fourier transform of the 1D transmission line model, is applied. Since the CRLH TLs are electrically thin, this model is adequate to describe transient phenomena. The method is validated experimentally for the case of matched and mismatched CRLH impulse delay lines. Excellent agreement between theory and experiments is obtained. Various complex dispersive phenomena are investigated, including pulse delay as a function of the modulation frequency, pulse compression, and temporal Talbot pulse rate multiplication.