The model family proposed by Gifi (1990) is a flexible framework for the analysis of multivariate data. The common properties shared by all Gifi-models are the specification of a loss function solved by alternating least squares and transformations of the variables which lead to quantifications of the categories. The latter issue implies the concept of “”optimal scaling”” and allows to account for the scaling level of the variables. Starting from the basic model of homogeneity analysis, we present various extensions in terms of rank restrictions (nonlinear principal component analysis) and restrictions on sets of variables (nonlinear canonical correlation analysis). We focus on recent methodological developments and on the R package “”homals”” that allows for the computation of these models and provides new visualization techniques of the results.