We present an overview of the pulse compression phenomenon obtained during the propagation of ultra-short pulses in common used optical waveguides. In the case of the silicon-on-insulator (SOI) waveguides, using the modified and realistic variational approach (MVA) that involves the Rayleigh’s dissipation function (RDF), we conduct the analysis of the compression mechanism on different input profiles. This study allows to show the effects of fourth-order dispersion (FOD), the nonlinear coefficients of absorption (nonlinear absorption) and the chirp, not only on symmetric and compact pulses but also on those with asymmetric profile as the Airy pulses. Indeed, considering the case of linear compression, the conditions of their occurrence are obtained. A relation between the FOD, the group-velocity dispersion (GVD) and the chirp is proposed in this way. In the nonlinear case, using the symmetric profiles as input pulses, we demonstrate a periodic compression induced by the interplay between the self-phase modulation (SPM) and the FOD. This appears as a new mode to generate the pulse compression phenomenon. Then, we show that when large values of the initial chirp and absorption coefficients as the two-photon absorption (TPA) present in these waveguides are considered, the compression mechanism is completely destroyed with at least the observation of one pulse amplification over a short distance of propagation before the pulse broadening. Finally, the study relating to the Airy pulses, leads rather to the reduction of the compression length induced by the SPM, the TPA and the free-carrier absorption (FCA) showing the pulse asymmetry influence.