Abstract : My main thesis work is to understand the origin of molecular Hydrogen (H2 ) emission in active phases of galaxy evolution. Spitzer space telescope observations reveal a new class of H2 -luminous galaxies with enhanced H2 line emission but where star formation is strongly sup- pressed. This is in sharp contrast with what is observed in standard star forming galaxies. The Stephan's Quintet (SQ) galaxy collision is a striking example I initially focus on. We present a scenario and a detailed model to account for the presence of H2 in the SQ giant shock, to characterize its physical state, and to describe its role as a cooling agent of a violent phase of galaxy interactions. In this scenario, the dissipation of the mechanical energy of the collision produces a multiphase medium where molecular gas fragments coexist with a hot ( ∼ 5 × 10^6 K), X-ray emitting plasma. Our model quantiﬁes the gas cooling, dust destruction, H2 formation and emission in the postshock multiphase gas. The dynamical interaction between the ISM phases drives a cycle where H2 is formed out of atomic gas that cools, and is excited repeatedly before being destroyed. A cascade of energy is associated with this cycle, in which the mechanical energy powers supersonic turbulence within the molecular gas. The H2 emission is associated with the dissipation of this turbulent energy. New results of mid-infrared and radio observations in the SQ shock are presented. These observations reveal that dust and CO emission gas is associated with the warm H2 seen by Spitzer, and that this gas is in an unusual physical state where star formation is suppressed. In addition, to test the scenario proposed for the formation of H2 in the SQ shock, I carry on a detailed observational study and modeling of the dust emission from the H2 gas. Observational perspectives with the Herschel satellite are discussed. These observations suggest that H2 contributes signiﬁcantly to the energy bugdet of galaxies which are in key phases of their evolution (galaxy interaction, gas accretion in galaxy clusters, starburst or AGN feedback). My thesis work is a ﬁrst step to understand the role that molecular gas plays in galaxy evolution. Our model developped for SQ is extended to the context of radio galaxies, which allow for the ﬁrst time to peer at the impact of the AGN-driven jet on the multiphase ISM of the host galaxy. A natural extension of this work is the characterization of the energetics of galactic winds (in the M82 starburst galaxy for instance) and in AGN-driven winds recently discovered in high-redshift radio-galaxies. This thesis includes the tools to perform a detailed modeling of Spitzer and upcoming Herschel data. Besides this work, as a member of the JWST/MIRI consortium, I also report my contribution to the optical performance tests of the MIRI instrument, which will extend the study of H2 -luminous galaxies to high redshifts. The observational and theoretical work presented in this manuscript may help to develop a phenomenological ”recipe” of the impact of H2 on the energetics of galaxy evolution. This work will certainly be helpful for the preparation of future observing programs aiming at testing this phenomenology directly, thanks to spectroscopy of high-redshift galaxies with the JWST and SPICA missions.