  We offer a short tour into the interactive interpretation of sequential
programs. We emphasize streamlike computation -- that is, computation of
successive bits of information upon request. The core of the approach surveyed
here dates back to the work of Berry and the author on sequential algorithms on
concrete data structures in the late seventies, culminating in the design of
the programming language CDS, in which the semantics of programs of any type
can be explored interactively. Around one decade later, two major insights of
Cartwright and Felleisen on one hand, and of Lamarche on the other hand gave
new, decisive impulses to the study of sequentiality. Cartwright and Felleisen
observed that sequential algorithms give a direct semantics to control
operators like \"call-cc\" and proposed to include explicit errors both in the
syntax and in the semantics of the language PCF. Lamarche (unpublished)
connected sequential algorithms to linear logic and games. The successful
program of games semantics has spanned over the nineties until now, starting
with syntax-independent characterizations of the term model of PCF by Abramsky,
Jagadeesan, and Malacaria on one hand, and by Hyland and Ong on the other hand.
