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Insurance schemes are a widely supported form of finance mechanism to address climate change-induced loss and damage and are part of the Warsaw International Mechanism for Loss and Damage. This paper reviews active insurance schemes for loss and damage by exploring existing critiques. Novel insights into the fundamental challenges that insurance schemes face are then examined, in particular in the context of common but differentiated responsibilities and respective capabilities, intergenerational equity, economic and gender inequality, and human mobility. The analysis concludes that, despite their popularity among policymakers, insurance schemes seem ill-suited to address the full range of loss and damage. Therefore, pursuing these schemes, without backstopping from international finance, might undermine the objective of responding to loss and damage in a comprehensive manner. Consequently, it may be advisable for policy makers to consider how to overcome the apparent challenges in order to ‘ensure the uninsurable’.