Label smoothing is commonly used in training deep learning models, wherein one-hot training labels are mixed with uniform label vectors. Empirically, smoothing has been shown to improve both predictive performance and model calibration. In this paper, we study whether label smoothing is also effective as a means of coping with label noise. While label smoothing apparently amplifies this problem --- being equivalent to injecting symmetric noise to the labels --- we show how it relates to a general family of loss-correction techniques from the label noise literature. Building on this connection, we show that label smoothing can be competitive with loss-correction techniques under label noise. Further, we show that when performing distillation under label noise, label smoothing of the teacher can be beneficial; this is in contrast to recent findings for noise-free problems, and sheds further light on settings where label smoothing is beneficial.