When detecting anomalous sounds in complex environments, one of the main difficulties is that trained models must be sensitive to subtle differences in monitored target signals, while many practical applications also require them to be insensitive to changes in acoustic domains. Examples of such domain shifts include changing the type of microphone or the location of acoustic sensors, which can have a much stronger impact on the acoustic signal than subtle anomalies themselves. Moreover, users typically aim to train a model only on source domain data, which they may have a relatively large collection of, and they hope that such a trained model will be able to generalize well to an unseen target domain by providing only a minimal number of samples to characterize the acoustic signals in that domain. In this work, we review and discuss recent publications focusing on this domain generalization problem for anomalous sound detection in the context of the DCASE challenges on acoustic machine condition monitoring.