Wewill first review the recentprogress in SYK models and their global impacts in quantum gravity, QCD, condensed matter physics and quantum information science. Then we will outline the results achieved in our recent works in [1-5]. This colloquium is pedagogical, so should be accessible to any graduate students who are interested in working on this still rapidly expandingresearch direction and other related directions such as many body localization (MBL), eigenstate thermalization hypothesis (ETH)， Complexity, Machine learning, etc.
1.Jinwu Ye,Two indicesSachdev-Ye-Kitaev model,ArXiv：1809.0667, substantially revised version 2 to be put on ArXiv soon
2.Fadi Sun, Yu Yi-Xiang, Jinwu Ye and WuMing Liu, A new universal ratio in Random Matrix Theory andRandom matrices and quantum analog of Kolmogorov-Arnold-Moser (KAM) theorem in hybrid Type-I and Type-II Sachdev-Ye-Kitaev models,ArXiv：1809.07577.
3.Fadi Sun， Yu Yi-Xiang, Jinwu Ye and WuMing Liu,Classifications of quantum chaos in colored Sachdev-Ye-Kitaev models, arXiv:1903.02213.
4.Fadi Sun and Jinwu Ye,Periodic Table of SYK and supersymmetric SYK , arXiv:1905.07694
5.Yu Yi-Xiang, Jinwu Ye and CunLin Zhang,Photon Berry phases, Instantons, Quantum chaos and quantum analog of Kolmogorov-Arnold-Moser (KAM) theorem in the $ U(1)/Z_2 $ Dicke models, arXiv:1903.02947