  A problem of Erd\H{o}s (Amer. Math. Monthly 52: 494-498, 1945) and a theorem
of Fejes T\'oth and Fejes T\'oth (Acta Math. Acad. Sci. Hungar. 24: 229-232,
1973) initiated the study of non-separable arrangements of convex bodies and
the investigation of totally separable packings of convex bodies with both
topics analyzing the concept of separability from the point view of discrete
geometry. This article surveys the progress made on these and some closely
related problems and highlights the relevant questions that have been left
open.
