© Koninklijke Brill NV, Leiden, 2021 | doi:10.1163/15507076-12340009 Heritage Language Journal 18 (2021) 1–37 brill.com/hlj On the Many Dimensions of Complexity in Heritage Languages Oksana Laleko Associate Professor, Linguistics Program and English Department, State University of New York at New Paltz, USA lalekoo@newpaltz.edu Gregory Scontras Associate Professor, Department of Language Science, University of California, Irvine, USA g.scontras@uci.edu Abstract Heritage languages are often discussed in terms of their (reduced) complexity, but few attempts have been made to objectively measure the complexity of heritage languages. Here we explore various approaches to the investigation of language complexity, dis- cussing three broad areas of inquiry: (i) attempts to objectively measure grammatical complexity, (ii) the potential role of socio-demographic factors in explaining vari- ability in complexity, and (iii) considerations beyond grammatical complexity, which include the various aspects of complexity invoked when language is used for the pur- pose of communication. At each point, we highlight potential wisdom to be drawn from existing studies of heritage languages, which help to inform hypotheses for future study. The upshot is that complexity in heritage languages is itself a complex phenomenon – an observation that calls into question traditional characterizations of heritage languages in terms of an overall decrease in complexity. Keywords complexity – heritage language – morphology – syntax – acquisition – processing