Abstract:  The Dark Energy Spectroscopic Instrument (DESI) is undertaking a five-year survey spanning 14,000 square degrees of the sky, with the goal of mapping 40 million extragalactic redshifts. These observations aim to refine our understanding of the universe’s expansion history through Baryon Acoustic Oscillations (BAO) and the growth of cosmic structure via Full Shape analyses. In 2024, the DESI collaboration released BAO (April 4) and Full Shape (November 19) cosmology results from the Data Release 1 (DR1) sample, assembled from the first year of data taking (2021 - 2022). This presentation will introduce the instrument and the survey and review the BAO and Full Shape measurements derived from DR1. I will discuss the cosmological constraints on the Hubble parameter, neutrino masses, dark energy and modified gravity obtained using DR1 data independently and in combination with complementary probes such as the CMB, supernova and weak lensing datasets. I will conclude by outlining potential improvements for standard analyses and providing an outlook on upcoming DESI future results.