This paper discusses topicality in Icelandic grammar as realized in several phenomena: referential third person pro drop in Old Icelandic, diverse types of topic drop in Old and Modern Icelandic and Narrative Inversion (declarative VS clauses), also in both Old and Modern Icelandic. These phenomena all involve aboutness topics, given topics or both, thus showing that distinct types of topicality are active in Icelandic. However, in contrast to Italian, Icelandic does not provide evidence that different topic types have different structural correlates, a fact that suggests that topicality types are not generally structuralized in language (while not excluding that a topicality hierarchy may be PF-licensed by externalization properties specific to languages like Italian). Topicality is presumably a universally available category or phenomenon, but it is plausibly an interface third factor phenomenon (in the sense of Chomsky 2005), not provided by Universal Grammar but interacting with it in the shaping of externalized grammar, differently so in different languages. *