Crystallisation starts off with nucleation, which is rather poorly understood. However, over the last few years there have been important quantitative experiments at constant supersaturation, and the modelling of this data has also advanced. Experiments in which the supersaturation is varying, e.g., those at constant cooling rate, are important but hard to interpret. This review focuses on the state of the art in quantitative studies of nucleation at constant supersaturation. We can now test reliably for heterogeneous nucleation and somewhat less reliably for the rarer case of homogeneous nucleation. In the case of heterogeneous nucleation, we can also obtain at least some information on what is responsible for nucleation. We also now have (unfortunately currently untested) predictions for the scaling of nucleation timescales with system size. These predictions may prove important both for scaling up from small droplets to larger volumes, and for scaling down to crystallisation at the nanoscales relevant for nanotechnology applications. Finally, it is worth noting that in many experiments the dynamic range of nucleation times is too large to be measured. This is presumably due to highly variable impurities, and this problem may need to be addressed in future work.