This dissertation is devoted to investigation of quantum chaos in the Sachdev-Ye-Kitaev (SYK) and supersymmetric SYK models. First, a unified minimal scheme is developed to classify quantum chaos in the SYK and supersymmetric SYK models and also work out the structure of the energy levels in one periodic table. The SYK with even q-body or supersymmetric SYK with odd q-body interaction, with N even or odd number of sites, are put on an equal footing in the minimal Hilbert space; N (mod 8), q (mod 4) double Bott periodicity, and a reflection relation are identified. Then, exact diagonalizations are performed to study both the bulk energy level statistics and hard-edge behaviors. Excellent agreements between the exact diagonalization results and the symmetry classifications are demonstrated. This compact and systematic method can be transformed to map out more complicated periodic tables of SYK models with more degrees of freedom, tensor models, or symmetry protected topological phases.