  Developments over the last two decades have opened the path towards quantum
technologies in many quantum systems, such as cold atoms, trapped ions,
cavity-quantum electrodynamics (QED), and circuit-QED. However the fragility of
quantum states to the effects of measurement and decoherence still poses one of
the greatest challenges in quantum technology. An imperative capability in this
path is quantum feedback, as it enhances the control possibilities and allows
for prolonging coherence times through quantum error correction. While changing
parameters from shot to shot of an experiment or procedure can be considered
feedback, quantum mechanics also allows for the intriguing possibility of
performing feedback operations during the measurement process itself. This
broader approach to measurements leads to the concepts of weak measurement,
quantum trajectories and numerous types of feedback with no classical
analogues. These types of processes are the primary focus of this review. We
introduce the concept of quantum feedback in the context of circuit QED, an
experimental platform with significant potential in quantum feedback and
technology. We then discuss several experiments and see how they elucidate the
concepts of continuous measurements and feedback. We conclude with an overview
of coherent feedback, with application to fault-tolerant error correction.
