  Much of our progress in understanding microscale biology has been powered by
advances in microscopy. For instance, super-resolution microscopes allow the
observation of biological structures at near-atomic-scale resolution, while
multi-photon microscopes allow imaging deep into tissue. However, biological
structures and dynamics still often remain out of reach of existing
microscopes, with further advances in signal-to-noise, resolution and speed
needed to access them. In many cases, the performance of microscopes is now
limited by quantum effects -- such as noise due to the quantisation of light
into photons or, for multi-photon microscopes, the low cross-section of
multi-photon scattering. These limitations can be overcome by exploiting
features of quantum mechanics such as entanglement. Quantum effects can also
provide new ways to enhance the performance of microscopes, such as new
super-resolution techniques and new techniques to image at difficult to reach
wavelengths. This review provides an overview of these various ways in which
quantum techniques can improve microscopy, including recent experimental
progress. It seeks to provide a realistic picture of what is possible, and what
the constraints and opportunities are.
