It is well established by now that computer science has a number of concerns in common with natural language understanding. Common themes show up in particular with algorithmic aspects of text processing. This chapter gives an overview of border crossings from NLP to CS and back. Starting out from syntactic analysis, we trace our route via a philosophical puzzle about meaning, Hoare correctness rules for dynamic semantics, error state analysis of presupposition, equational reasoning about state change, programming with frameworks originally devised for natural language semantics, and the logic of incremental processing. In many cases methods and perspectives developed on one side of the border proved quite useful on the other side, although usually it becomes clear after a while that tools have to be redesigned to fit. The chapter ends with a sketch of the emerging contours of a ‘proper treatment of context in natural language’ that is more than just an application of a logic designed for program analysis.