Modelling, particularly computer-based modelling, is increasingly used in political, managerial, and scientific contexts to enable and justify decisions. Technocratic decision makers also aspire to understand and incorporate local knowledge, albeit at times only superficially. We analyse one consequence of this situation - ongoing attempts to formalise, synthesize and integrate local and/or indigenous knowledge into models. Field experience of knowledge projects with Indigenous Australians underpins our analysis, but we primarily discuss a priori and general issues: the political and ethical context of such projects; knowledge making as terminology; key characteristics of (scientific) models; local capacity, participation, and representation; and examples of computer-based tools for knowledge representation. Such formal abstractions will always be controversial, but demand for them seems likely to continue. To improve interdisciplinary understanding of what might be entailed by genuine attempts to meet that demand, our paper provides signposts to and analysis of important features of local ecological knowledge modelling.