Summary: Structuring logic programs to deal with evolving and incomplete knowledge is one of the main issues in representing knowledge with logic. On the one hand, evolving knowledge in logic programming can be modelled through suitable operators for the dynamic composition of separate programs. On the other hand, when dealing with dynamic compositions of logic programs, the open world assumption adequately models the aspects of incompleteness of knowledge. We analyse the notion of open program along with suitable operators for composing and closing programs. We present the semantics of open programs and of the associated operators in two different, equivalent styles. We define a model-theoretic semantics in term of Herbrand models, while an operational semantics is given by means of inference rules. In the second part of the paper, we explore some applications of open programs and of their compositions. We show how a number of policies for structuring logic programming can be reconstructed in this setting, including the construction of modules with import declarations. Finally, the relations between open programs and abductive logic programming are discussed.