Ever since the discovery of galaxies, understanding their formation and evolution through cosmic time is one of the major challenges in modern astrophysics. During the last 15 years, substantial theoretical and observational evidence has shown that the majority of galaxies form well-known and relatively tight scaling relations. These include a relation between the star formation rate (SFR) and the stellar mass, dubbed the main sequence (MS) of star formation, and between the SFR and gas surface densities, known as the Schmidt-Kennicutt relation. These regularities underlying the observed properties have brought us to argue that the bulk of the stellar growth in galaxies mainly occurs through secular and steady evolution. A minor fraction of star-forming galaxies, named starbursts, are located well above the MS at all redshifts, where their extreme star formation is thought to be ignited following violent collisions. Although the details of the mechanisms responsible for triggering and quenching the star formation activity in main-sequence and starburst galaxies are still debated, it is clear that the available amount of molecular gas plays a major role in both these processes, since it constitutes the fuel for the birth of new stars. Therefore, accurate estimates of the gas mass and fraction in galaxies are key to interpret the buildup of stellar mass, and how the gas is transformed into stars. Quantifying the amount of molecular gas in galaxies has proved to be a major challenge for astrophysicists due to the lack of direct observables of H2, the most abundant molecule in the Universe. As a consequence, we have to rely on indirect tracers, traditionally being carbon monoxide (CO) and dust. However, the use of these proxies suffers from uncertainties and degeneracies that prevent us from reaching definitive conclusions about the processes mentioned above. Exploring alteriii native tracers is thus imperative to reach a coherent picture of the interstellar medium (ISM) properties of galaxies.The first part of this thesis is dedicated to this explorat ion. Specifically, I will compare the gas content using the classical CO and dust tracers with the emission from polycyclic aromatic hydrocarbons (PAHs). I will present evidence supporting the existence of a universal linear relation between the emission from PAHs and CO for galaxies on and above the MS. This relation implies that the PAH/CO luminosity ratio is independent of the star formation efficiency (SFE). This is at odds with the infrared/PAH luminosity ratio, which is rising with increasing SFE. In addition, a stronger correlation is found between the emission from PAHs and cold rather warm dust. All these results indicate that PAHs can trace the molecular gas mass similarly to CO and dust, rather than the total SFR, as commonly thought in the classical picture. This may impact future studies, as PAHs will be readily detectable up to z ∼ 3.5 with the James Webb Space Telescope.In the second part, I will focus on the dust and gas propertie s of a typical distant starburst galaxy to address several puzzling findings emerged during the last few years. These include unphysically large dust-to-stellar-mass ratios, which are inconsistent with the current models of dust production and destruction, in addition to surprisingly cold dust temperatures and faible radiation fields that are below that of main-sequence galaxies at similar redshift. As these extreme galaxies go through intense bursts of star formation activity, forming up to thousands of solar masses per year, these properties are perplexing. The latter are generally derived from sparse far-infrared spectral energy distributions (SEDs) and under the assumption of optically thin dust emission. However, a free opacity model provides an equally good description of the FIR SED, but with radically different implications on the physical properties of the dust. In this thesis, I will present a new method that can potentially break the degeneracy between optically thin and thick solutions. This method relies on the empirical correlation between the dust temperature and the gas excitation temperature derived from the neutral atomic carbon lines, [C I]. By means of new NOEMA observations, we will test this concept for a z = 4 starburst galaxy for which the [C I] gas temperature favors an optically thick solution, alleviating the observed tensions by returning a warmer dust temperature and a lower mass. The last part of this thesis will be dedicated to future developments of the methods presented here to bring them to full maturity. I will also introduce preliminary results of an ongoing project aimed at studying the radio and FIR emission in a sample of spectroscopically confirmed massive quiescentgalaxies in the distant Universe, in order to investigate the presence of active galactic nuclei and possible residual pockets of dust, and gain insight into the physics of quenching. A brief introduction of this project will be presented in the last chapter.