The growth of dark matter halos is to first-order the main driver of galaxy formation in our standard cosmological model. Yet, complex and highly non-linear baryonic processes take over at the centers of these halos, leading to the diversity of galaxies observed in the Universe today. The coupling between baryonic and dark matter physics is central to our understanding of galaxies and yet, it remains a challenge both for theoretical models and observations. In particular, whether, how and why observed properties of galaxies are influenced by the properties of their host dark matter halos remain open questions in the field. The main aim of this thesis is to explore the formation and evolution of galaxies in their cosmological context and environment by answering these fundamental questions observationally, mainly through stellar population analysis. Stellar populations within galaxies are fossil records which encode information about the evolutionary past of the galaxies, which have been traditionally studied in terms of  baryonic properties alone. Our work combines detailed stellar population measurements with different halo characterizations to investigate the role of dark matter halos in modulating observed properties and key scaling relations of galaxies in the Local Universe.

We probed how stellar population properties and star formation histories depend on halo mass for central galaxies from the large spectroscopic survey SDSS. We map galaxy ages, metallicities across the stellar-to-halo mass relation and velocity dispersion - halo mass relation using their absorption optical spectra. We find that these observables correlate with the scatter of both relations, but velocity dispersion is a better predictor of these properties than stellar mass. Most interestingly, our findings indicate that for a given stellar mass or velocity dispersion, galaxies have different stellar populations depending on the mass of their host halos. Galaxies in less massive halos are older and more metal-rich at fixed stellar mass, and we also find that they form the bulk of their stars early on and over short-timescales according to their star formation histories. On top of that, we introduced a new observational approach using galaxies from CALIFA integral-field spectroscopic survey to assess the role of total dynamical mass as an alternative metric sensitive to their dark matter content. These total masses are derived through detailed Jeans dynamical modelling of the stellar kinematics of the galaxies, and incorporate both a stellar and a dark matter component to be able to reproduce the stellar motions. In addition to stellar populations, we also investigate the stellar angular momentum, star formation rates and galaxy morphology across the stellar-to-total dynamical mass relation. Similarly as for the stellar-to-halo mass relation, we observe that all these galaxy properties sensitive to different time-scale of the galaxy formation process depend both on stellar mass and total mass, with these two quantities being derived in a completely independent manner. Galaxies become older, more metal-rich and less rotationally supported, have lower star formation rates and earlier-type morphologies as their total mass decreases, at fixed stellar mass.

Additionally, we investigated the origin of the scaling relation between global star formation rates and galaxy stellar masses, the star-forming main sequence. We explore the connection between the scatter of this relation and star formation histories for SDSS central galaxies using their absorption optical spectra. We observe that for a given stellar mass, galaxies have experienced different star formation histories depending on their present-day star formation rates. Galaxies with higher star formation rates today have more extended star formation histories, while the ones with lower star formation rates have formed the bulk of their stars earlier on and faster.

We interpret our results in the context of the evolution of the host dark matter halos of the galaxies over cosmic time. We speculate that the halo formation times drives the observed trends across the stellar-to-halo mass relation, stellar-to-total dynamical mass relation and the star forming main sequence, with the scatter of these relations mapping galaxies/halos at different evolutionary stages.

Furthermore, we inspected whether the numerical large-scale cosmological hydrodynamical simulations can reproduce observed local fundamental metallicity relation, i.e., the anti-correlation between gas-phase metallicities and star formation rates seen in low mass galaxies at local scales. We generate spatially resolved maps of gas-phase metallicity and star formation rate for disc EAGLE galaxies. Low mass galaxies show regions have low star formation rates have enhanced gas-phase metallicities, while this trend reverse for massive galaxies, in agreement with integral-field spectroscopic observations. Lastly, we also explored the origin of the gas fuelling star formation in EAGLE galaxies at two cosmic epochs, present-day and cosmic noon, by tracking star-forming gas and recently formed stars back in time. The majority of the gas that sustains star formation in galaxies at both redshifts was already in the galaxies about one Gyr before star formation. We find that the contribution of accreted gas coming from mergers increases at cosmic noon with respect to present-day. Yet, the contribution of gas with cosmological origin (e.g., mergers with dark and luminous halos) is relevant for low mass galaxies today, showing that cosmological gas accretion is an important source to fuel star formation in these low mass halos not only at high redshifts.