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.