In this paper, we describe the SemEval-2010 shared task on "Linking Events and Their Participants in Discourse". This task is a variant of the classical semantic role labelling task. The novel aspect is that we focus on linking local semantic argument structures across sentence boundaries. Specifically, the task aims at linking locally uninstantiated roles to their co-referents in the wider discourse context (if such co-referents exist). This task is potentially beneficial for a number of NLP applications and we hope that it will not only attract researchers from the semantic role labelling community but also from co-reference resolution and information extraction.