Optical imaging has had a central role in elucidating the underlying biological and physiological mechanisms in living specimens owing to its high spatial resolution, molecular specificity and minimal invasiveness. However, its working depth for in vivo imaging is extremely shallow, and thus reactions occurring deep inside living specimens remain out of reach. This problem originates primarily from multiple light scattering caused by the inhomogeneity of tissue obscuring the desired image information. Adaptive optical microscopy, which minimizes the effect of sample-induced aberrations, has to date been the most effective approach to addressing this problem, but its performance has plateaued because it can suppress only lower-order perturbations. To achieve an imaging depth beyond this conventional limit, there is increasing interest in exploiting the physics governing multiple light scattering. New approaches have emerged based on the deterministic measurement and/or control of multiple-scattered waves, rather than their stochastic and statistical treatment. In this Review, we provide an overview of recent developments in this area, with a focus on approaches that achieve a microscopic spatial resolution while remaining useful for in vivo imaging, and discuss their present limitations and future prospects.