Jiaxi Yu is a current Ph.D. candidate at the Laboratory of Astrophysics at EPFL, Lausanne, Switzerland, with research interests in observational cosmology, large-scale structure of the universe. She studies the galaxy-halo connection of galaxies and quasars from spectroscopic surveys like SDSS and DESI. She is also interested in quantifying the observational systematics on those surveys for the two-point correlation function that is key for cosmological measurement like Baryonic Acoustic Oscillation and Redshift Space Distortion.LCDM is the standard model of modern cosmology with two dark components, dark matter and dark energy. The nature of dark energy and the dark matter structure growth rate can be probed via the large-scale structure (LSS). For this purpose, we observe millions of spectra of galaxies and quasars (QSOs) with spectroscopic galaxy surveys to explore the 3D map of the Universe. Meanwhile, high-resolution N-body simulations can reproduce the theoretically predicted LSS and provide properties of the clustered dark matter (haloes). The relation between galaxy/quasar-haloes is highly non-linear and subject to the local environment, and is also crucial for accurate cosmological measurements. SubHalo Abundance Matching (SHAM) is an empirical method to assign galaxies to dark matter (sub)haloes from N-body simulations. However, its classical version only works for luminous red galaxies (LRGs, most of which are quiescent). In this talk, we introduce a generalized SHAM for LRGs,  emission line galaxies (ELGs, mostly star-forming) and QSOs, accounting for the massive (sub)halo incompleteness, the redshift uncertainty and the satellite fraction. Its model galaxies reproduce all the observed clustering of DESI LRGs, ELGs and QSOs on scales of 5-30Mpc/h and at 0.4<z<3.5. The algorithm can be easily transferred to a multi-tracer SHAM for cosmological measurement and cosmic web studies and is important for neutrino mass and modified gravity studies by removing the redshift uncertainty bias. In addition to this method, other work on DESI galaxy-halo connection with Halo Occupation Distribution (HOD) and Stellar-Halo-Mass Relation (SHMR) will also be introduced. They reveal interesting properties of the dark matter tracers of DESI and present consistent halo properties for the same tracer across different methods.