In this presentation, I will introduce our recent works in the fields of cavity and waveguide quantum electrodynamics (QED). On the one hand, in the field of cavity QED, we proposed a new type of cavity QED system, which allows us to exponentially enhance the single-atom cooperativity parameter. It overcomes the Q-V trade-off, i.e., Q being directly proportional to V, in the conventional cavity QED systems. We also studied the nonreciprocal quantum effects in cavity QED, including the nonreciprocal superradiant phase transitions and bundle emission. On the other hand, in the field of waveguide QED, we investigated the chiral interaction and the disorder of atoms array induced strongly correlated photons. We found that the chiral cavity-waveguide interaction or the disorder in the transition frequencies of qubits can induce photon antibunching, especially nearly perfect photon blockade events. We also will introduce our recent work regarding the exotic long-range interaction and the associating quantum manybody phases in topological waveguide QED system. Our works is of fundamental interest in expanding the fields of cavity and waveguide QED, and has potential applications in the on-chip quantum information science and quantum simulation of strong correlated matters.