It is well-known that large logarithms arise in scattering amplitudes at all orders in perturbation theory, that have to be summed up to all orders (“resummed") in order to produce reliable collider predictions. These terms arise when emitted gauge bosons become “soft" (have zero 4-momentum), and many approaches exist for classifying them. Until recently, much less was known about how to go beyond this approximation. This is important for improving the precision of QCD predictions, but is also of more formal interest in both QCD and gravity, as exemplified by recently conjectured next-to-soft theorems. This talk will summarise approaches for describing next-to-soft corrections to amplitudes, including the relationship between the more formal, and the more phenomenologically-minded techniques. I will give an example of how to classify such effects in Drell-Yan production, before commenting on the similarities between QCD and gravity.