For several decades, the topics of the title have had a fruitful interaction.The talk will survey some of these connections that have been of interest to the speaker, including the GB/GC classification of convex bodies, Ito-Nisio singularities from a geometric viewpoint, Gaussian representation of intrinsic volumes, Gaussian samples and random projection of regular simplices, the Wills functional in a Gaussian context, deviation inequalities, and metrization of convex bodies.