Chaotic and topological phenomena have totally opposite characteristics: the former/latter are extremely sensitive to/robust against the change in system's details (e.g., the parameters of the Hamiltonian and the initial conditions). Thus they are commonly considered not to be compatible. In this talk, starting from discussions on how revisiting Bloch's band structure theory motivates me to investigate topological phenomena in quantum chaos, I will show how, by introducing a spin degree of freedom to the canonical model of chaotic dynamics, the so-called quantum kicked rotor (QKR), which is simply a particle moving on a ring and subjected to pulsed external force, rich dynamical behaviors of topological origin arise. These include, notably, the realization of quantum Hall physics and Haldane conjecture, which occur originally to totally different systems, namely, many-electron systems and quantum antiferromagnetic chains, respectively. I will show how a supersymmetry structure arises from the time-driving nature of QKR, and serves as a seed for a wealth of topological phenomena in this chaotic system as simple as being single-particle.