This paper discusses the contribution of Cerioli et al. (Stat Methods Appl, 2018), where robust monitoring based on high breakdown point estimators is proposed for multivariate data. The results follow years of development in robust diagnostic techniques. We discuss the issues of extending data monitoring to other models with complex structure, e.g. factor analysis, mixed linear models for which S- and MM-estimators exist or deviating data cells. We emphasise the importance of robust testing that is often overlooked despite robust tests being readily available once S- and MM-estimators have been defined. We mention open questions like out-of-sample inference or big data issues that would benefit from monitoring.