One of the most ubiquitous and technologically important phenomena in nature is the nucleation of homogeneous flowing systems. The microscopic effects of shear on a nucleating system are still imperfectly understood, although in recent years a consistent picture has emerged. The opposing effects of shear can be split into two major contributions for simple liquids: increase of the energetic cost of nucleation, and enhancement of the kinetics. In this review, we describe the latest computational and theoretical techniques which have been developed over the past two decades. We collate and unify the overarching influences of shear, temperature, and supersaturation on the process of homogeneous nucleation. Experimental techniques and capabilities are discussed, against the backdrop of results from simulations and theory. Although we primarily focus on simple liquids, we also touch upon the sheared nucleation of more complex systems, including glasses and polymer melts. We speculate on the promising directions and possible advances that could come to fruition in the future.