The Dark Energy Spectroscopic Instrument (DESI) is leading a groundbreaking five-year survey to investigate the influence of dark energy on cosmic expansion and the evolution of large-scale structure. Latest baryon acoustic oscillations (BAO) and Full-Shape measurements and cosmological results from DESI will be presented and discussed, based on three years of observations. We considered both solely the data from the survey and in combination with cosmic microwave background (CMB), supernovae (SNe), Big Bang Nucleosynthesis (BBN) priors, and 3x2pt measurements observations. We focused on the measurement of constraints on expansion rate, with particular attention on the comparison with Planck results considering ΛCDM model, on dark energy equation of state and on finding upper limits for the sum of neutrino masses. Y3 BAO results are well described by a flat ΛCDM model, but in ΛCDMthe tension between the DESI+BBN and SH0ES H0 results now stands at 4.5σ independent of the CMB, and now the parameters preferred by BAO are in mild 2.3σ tension with those determined from the cosmic microwave background (CMB). This tension is alleviated by dark energy with a time-evolving equation of state parametrized by w0 and wa, where this solution is preferred over ΛCDM at 3.1σ for the combination of DESI BAO and CMB data and up to 2.8 − 4.2σ when including also SNe (depending on which sample is used). These results provide a critical assessment of the standard cosmological model. Regarding Y1 Full-Shape results on S8, we observe an excellence agreement between our data and CMB, both of which are slightly higher than values inferred the weak lensing survey. This tension is alleviated considering the combination with 3x2pt information from DESY3. Finally, regarding constraints on modified gravity, DESI data alone can constrain only μ0, however, the combination with CMB and information from lensing allows us to constrain Σ0 as well, obtaining GR-compatible results. However, although it is an effect not given by the DESI data, it’s interesting to point out that the use of different versions of the Planck likelihood leads to appreciable variations in the estimate of Σ0 due to differences in lensing potential estimations, even going as far as having a 3σ tension compared to the GR previons in the most extreme case.