  Adaptive optics has made significant advancement over the past decade,
becoming the essential technology in a wide variety of applications,
particularly in the realm of quantum optics. One key area of impact is
gravitational-wave detection, where quantum correlations are distributed over
kilometer-long distances by beams with hundreds of kilowatts of optical power.
Decades of development were required to develop robust and stable techniques to
sense mismatches between the Gaussian beams and the resonators, all while
maintaining the quantum correlations. Here we summarize the crucial
advancements in transverse mode control required for gravitational-wave
detection. As we look towards the advanced designs of future detectors, we
highlight key challenges and offer recommendations for the design of these
instruments. We conclude the review with a discussion of the broader
application of adaptive optics in quantum technologies: communication,
computation, imaging and sensing.
