One-nodal degenerations of Fano threefolds

There are two sorts of 1-nodal degenerations of Fano 3-folds, factorial and non-factorial. I will describe a classification of such degenerations for 3-folds of Picard rank 1, emphasizing an interesting relation with smooth Fano 3-folds of higher Picard rank. This is a joint work in progress with Yu. Prokhorov.