The Earth system may react in a nonlinear threshold response to climate forcings. Incorporating threshold responses into integrated assessment models (IAMs) used for climate policy analysis poses nontrivial challenges, for example due to methodological limitations and pervasive deep uncertainties. Here we explore a specific threshold response, a potential disintegration of the West Antarctic Ice Sheet (WAIS). We review the current scientific understanding of WAIS, identify methodological and conceptual issues, and demonstrate avenues to address some of them through a stochastic hazard IAM framework combining emulation, expert knowledge, and learning. We conclude with a discussion of challenges and research needs.