The goal of this thesis project is to address the questions: (1) How does the molecular gas content of galaxies evolve over cosmic time?, (2) How long can massive star forming clumps, as are found in galaxies at z ~ 1–3, survive before they are dissipated by stellar feedback, and is this timescale long enough for the clumps to have an important role in the evolution of the galaxy?, and (3) What can we learn about star formation in clumpy, gas-rich, turbulent galaxies, from the resolved Kennicutt-Schmidt law? To address these questions, I combine observations from both the high- and low-redshift universe. To constrain the evolution of molecular gas content in galaxies out to a redshift of ~4, I use a sample of 110 normal main sequence galaxies that have been observed in CO as part of the second Plateau de Bure High-z Blue-Sequence Survey (PHIBBS2), to identify previously unknown sources in the data. I then use these serendipitous detections to construct the CO luminosity functions for transitions ranging from CO(2-1) to CO(6-5), over the redshift range of z ~ 0.5 - 4. The molecular gas density evolution constraints that I derive in this way are consistent with previous blind survey results, demonstrating the feasibility of using existing observations for this purpose. Many observations are difficult or not possible to do at high redshifts, therefore the remainder of this thesis involves studying molecular gas properties in a sample of nearby galaxies whose properties are more similar to z ~1 - 3 main sequence star forming galaxies than local systems. I will present new 0.15" resolution HST observations of six rare local (z ~ 0.1) galaxies (DYNAMO) observed to have turbulent, clumpy disks, making them much more similar to high-z main sequence galaxies than they are to other local ones. The choice of filters allows me to measure colors which are sensitive to changes in stellar population age and extinction, respectively. Colour measurements resolved at the clump scale show that most clumps in the DYNAMO sample I study show signs of young“cores” surrounded by older stellar populations, with only small variations in extinction. Finally, I will present results of ALMA CO observations of a sample of six DYNAMO galaxies, where the resolution of the observations allows for the derivation of a resolved Kennicutt-Schmidt law. Since these targets are selected to have gas fractions, star formation rates, and velocity dispersions similar to z ~ 1 - 3 galaxies, this allows me to study star forming clumps on scales that are not achievable at the peak of cosmic star formation..