Definitions vary, but broadly we can think about:

Crossdisciplinary as involving a team from different disciplines working together but hanging on to their own discipline standpoints.

Interdisciplinary as involving a deeper level of exchange between disciplines and perhaps using the fruits of collaboration to shift the boundaries of one’s own disciplines.

Transdisciplinary as involving a more full on willingness to engage with problems rather than disciplines and to create new conceptions of knowledge.

These terms are mostly discussed in the context of research teams but these are of course standpoints that an individual researcher can take. Debates range but we can see the pros the cons in terms of mirror images, for example the benefit of an interdisciplinary approach may be an invitation to think in new ways but a disadvantage may be the lack of engagement with body of knowledge within a particular discipline. In contrast a disciplinary approach may be more rooted in past literature but leave researchers trapped into a set way of looking at things.

If you are excited by Interdisciplinarity then try this article Ten cheers for Interdisciplinarity. As you read consider how you would provide the critique of interdisciplinary missing in the article.

Nissani, M. (1997) Ten cheers for interdisciplinarity: The case for interdisciplinary knowledge and research, The Social Science Journal, 34, 2, 1997, 201–216.