ABSTRACT
This survey paper is an extended version of a talk given at the “Algebra and Model Theory” Conference in Dresden, on June 1995. It presents what is known about the structure of the commutative monoid Unis(R) of the isomorphy classes of uniserial modules over a valuation domain R. The existence of nonstandard uniserial modules makes this structure more attractive. The included map of the existence problem of these modules shows when the structure of Unis(R) is enriched by nonstandard uniserials.
