1. Kristinsson's most recent project concerns the nature of prescriptivism, the interplay between description and prescription in linguistics, and the deconstructing of the prevailing descriptivist-prescriptivist binary (cf. Kristinsson 2023, 2021).
2. A good many publications by Kristinsson report on his investigations into language policy and planning, language ideologies, and language situation and practices. Kristinsson has largely adopted Spolsky's (2004) theoretical principles, adhering to the general approach that language policy is made up of three interrelated, yet independent, components, i.e., language practices, beliefs/ideologies, and planning. Cf., e.g., Kristinsson 2022a,b, 2021a, 2020, 2019a, 2018a,b, 2017a, 2016b, 2014a,b, 2013a, 2012c, 2010a, 2007; Kristinsson & Hilmarsson-Dunn 2012; Hilmarsson-Dunn & Kristinsson 2010, 2013).
3. Styles, and style-shift: Kristinsson's (2009) PhD thesis on language use in spoken media was based on his research into variation in the use of different linguistic features in two different genres of Icelandic radio language. Other projects include research into speaker evaluation of different features of Icelandic language use in different text genres (Kristinsson & Hilmarsson-Dunn 2013, 2015), and style-shifting (Kristinsson 2021).
4. Language choice in the academia and at HEIs. Cf. Kristinsson (2014); Kristinsson & Bernharðsson (2014a, 2014b).
5. Comprehension of legal texts. Cf. Kristinsson et al. (2022, 2018).

Among Kristinsson's earlier research interests is phonetics and phonology, historical phonology, terminology, lexicography, word formation, orthographic conventions, and variation in language.

Former professions

1996–2006 Director, The Icelandic Language Institute
1993–1996 Language consultant, RÚV Icelandic State Broadcasting Service
1990–1992 Linguist, Icelandic Language Institute [Deputy director 1991]
1984–1990 Upper secondary school teacher

1984-2023 Part time university teacher, University of Iceland, on and off, as follows: 
1984- Mostly courses at the programme for Icelandic as a second language (language use & pronunciation)
1990- Mostly courses at the department of Icelandic, on Icelandic phonetics and phonology, historical phonology, and applied linguistics
2000- Mostly courses at the department of Icelandic, on language use and sociolinguistics

1982-1987 Temporary assistant at different linguistic projects, as follows:
1982: University of Iceland Lexicography Project
1983-1984: Jónsson's Linguistic Computing Project & Dictionary of Synonyms
1987: The Icelandic Language Institute & Orthographic Dictionary

Various commissions of trust. Among other things the following:
2024-   Member of the Executive Committee of the European Federation of National Institutions for Language (EFNIL)

2006-2023 Head of Language Planning Department at the Árni Magnússon Institute for Icelandic Studies

2021- One of two project managers of the annual European Master Thesis Awards competition, under the aegis of The European Federation of National Institutions for Language (EFNIL)
2013–2015 Chairman of the Icelandic Linguistics Society
2011–2015 Vice Chairman of the Icelandic Sign Language Council
2008- External examiner at the programme for Icelandic as a second language at University of Iceland
2002- External examiner in tests for prospective certified translators and interpreters
2000–2006 Board member at the Nordic Institute in Finland (Nifin) [Chairman 2003–2004]
1998–2011 Nordic Secretary for the Icelandic Language Council
1998–2006 Chairman of the Icelandic Place Names Council
1995–1997 Chairman of the Icelandic Linguistics Society