Dr. Fangzhou Jiang is an assistant professor at the Kavli Institute for Astronomy and Astrophysics, Peking University. He obtained his PhD from Yale University in 2016, and was a PBC Fellow in the Hebrew University of Jerusalem from 2016 to 2019, a Troesh Scholar at Caltech with a jointly appointed Theory Fellow at the Carnegie Observatories from 2020 to 2022, before joining KIAA in 2023. Fangzhou carries out theoretical and computational studies of galaxies and cosmology. His research programs aim at a comprehensive theoretical picture of dark-matter halos and their interplay with inhabitant galaxies across the history of the Universe, with the ultimate goal being to constrain the properties of dark matter and to understand galaxy evolution all the way from the cosmological large scales down to sub-galactic small scales. Homepage: fzjiang.comThe ΛCDM paradigm of structure formation is successful on cosmological large scales but confronts challenges on sub-galactic small scales, regarding the number count, the internal structure, and the spatial distributions of dwarf galaxies and satellite galaxies. In this talk, I present semi-analytical and numerical efforts in quantifying these small-scale puzzles, within the concordance cosmology and in an alternative cosmology consisting of self-interacting dark matter. I discuss frontier trial solutions in the baryonic sector and in the dark sector and compare their pros and cons.