This article describes the evolution of applied exponential family models, starting at 1972, the year of publication of the seminal papers on generalized linear models and on Cox regression, and leading to multivariate (i) marginal models and inference based on estimating equations and (ii) random effects models and Bayesian simulation-based posterior inference. By referring to recent work in genetic epidemiology, on semiparametric methods for linkage analysis and on transmission/disequilibrium tests for haplotype transmission this paper illustrates the potential for the recent advances in applied probability and statistics to contribute to new and unified tools for statistical genetics. Finally, it is emphasized that there is a need for well-defined postgraduate education paths in medical statistics in the year 2000 and thereafter.
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