This paper presents a contribution to the development of a theory of CSCL scripts, i.e., an understanding of what happens when learners engage in such scripts. It builds on the Script Theory of Guidance (SToG) recently proposed by (Fischer et al. in "Educational Psychologist," 48(1), 56-66, 2013). We argue that, when engaged in a collaborative situation structured by a CSCL script, what learners consider is not "the script", but their appropriation of the script. Appropriation is a complex cognitive process which plays a role in both the recognition/conceptualization of the task to be achieved and its enactment, and is not dependent on the script only: it may be influenced by different external aspects. Therefore SToG and, actually, any theoretical framework attempting to provide an explanation of what happens when learners engage in CSCL scripts, should take into account appropriation issues. We develop our argumentation by focusing on technology-related aspects of appropriation and the role of institutional, domain and motivational aspects.