In this dissertation, we present results connecting the morphological evolution of galaxies and the decline of the star formation rate density in the Universe since z ∼ 2. For our study, we used the high-resolution HST/ACS images of the COSMOS survey to perform non-parametric automated morphological measurements on all objects with brightness I_F814W ≤ 23 mag (AB) in the 2 □° field, and combined these data with UV-photometry extracted from GALEX imaging to trace objects with moderate to high star formation rates. By first looking at the morphological properties of a sub-sample of z ∼ 0.7 galaxies, we discover that the morphological bimodality is already in place, that z ∼ 0.7 galaxies have masses, sizes and morphologies similar to that of local galaxies, but that they have star formation rates higher than local galaxies by a factor 2.5–3.5, independently of their other physical properties. We infer that the decline of the star formation rate density in the past 6 Gyrs can be mostly accounted for by a global fading of the galaxy population. We discover that morphology correlates well with UV-optical color, but that there also exists a population of red and dusty star-forming galaxies with bulge-like morphologies. We conclude that bulge growth is linked with episodes of high star formation, and interpret these objects as late-phase mergers. By studying the evolution of the luminosity function at 1500Å, we confirm the fading of the characteristic FUV magnitude of galaxies since z = 2.0, and discover a flattening of the faint-end slope at z < 0.7. We interpret this flattening as due to a decrease in the birth rate of galaxies. The morphological composition of our UV-sources indicates that disk galaxies dominate the FUV-luminosity function at all redshifts and all luminosities while interacting systems and galaxies with bulges contribute significantly mostly at the bright-end. Early-type disks appear to be the ones to evolve the most since z ∼ 0.7, an epoch through which their faint-end slope steepens. We interpret this as an indication that most small to intermediate-size disk galaxies formed their bulges in the last 6 Gyrs. Finally, we observe, at z > 1, a progressive increase, with redshift, of the contribution of bulge-dominated galaxies to the bright-end of the FUV-luminosity function, a likely signature of the epoch of bulge formation.