Until a few years after the turn of the century, almost all work on clustering and classification using mixture models had been based on Gaussian mixture models (e.g., Banfield and Raftery, 1993; Celeux and Govaert, 1995; Ghahramani and Hinton, 1997; Tipping and Bishop, 1999; McLachlan and Peel, 2000b; Fraley and Raftery, 2002b). Furthermore, what little work there was on non-Gaussian mixtures was on mixtures of multivariate t-distributions (e.g., McLachlan and Peel, 1998; Peel and McLachlan, 2000). A little beyond the turn of the century, work on t-mixtures burgeoned into a substantial subfield of mixture model-based classification (e.g., McLachlan et al., 2007; Andrews et al., 2011; Andrews and McNicholas, 2011a,b, 2012; Baek and McLachlan, 2011; McNicholas and Subedi, 2012; Steane et al., 2012; Lin et al., 2014). Around the same time, work on mixtures of skewed distributions took off, including work on skew-normal mixtures (e.g., Lin, 2009; Lin et al., 2016), skew-t mixtures (e.g., Lin, 2010; Lee and McLachlan, 2011, 2014; Vrbik and McNicholas, 2012, 2014; Murray et al., 2014a), shifted asymmetric Laplace mixtures (Franczak et al., 2014), variance-gamma mixtures (McNicholas et al., 2014), multivariate normal-inverse Gaussian mixtures (Karlis and Santourian, 2009; Subedi and McNicholas, 2014; O'Hagan et al., 2016), and generalized hyperbolic mixtures (Browne and McNicholas, 2015).