The occurrence and interpretation of negative variance components in the context of linear mixed models is well understood at this point, even though the issue is surrounded by subtle issues for estimation and testing (Verbeke and Molenberghs 2003, Molenberghs and Verbeke 2007). Broadly, negative variance components often point to negative within-cluster correlation. It is even possible to give such linear mixed models a meaningful hierarchical interpretation (Molenberghs and Verbeke 2011). Matters are more complicated when the outcomes are non-Gaussian, either in the context of the generalized linear mixed model, or extensions thereof that allow for flexible modeling of both within-unit correlation as well as overdispersion (Molenberghs et al. 2010). An additional complication is that, in practice, not only negative variance components due to negative correlation, but also underdispersion instead of overdispersion can occur, sometimes even jointly. With focus on both continuous and count data, we describe how models can be made sufficiently flexible and, in a number of cases, interpreted hierarchically (Luyts et al. 2017).