Global economic models have been increasingly used to project food and agricultural developments for long term-time horizons, but food security aspects have often been limited to food availability projections. In this paper, we propose a broader framework to explore the future of food and nutrition security with a focus on food availability, food access, and a reasonable proxy for food utilisation. This framework is applied to a new set of stakeholder-designed scenarios of alternative future worlds that were developed for the FOODSECURE project and are structured around the two dimensions of inequality and sustainability. The framework is tested with two global models, MAGNET-IMAGE and GLOBIOM, and illustrated through an assessment of the possible trade-offs between food and nutrition security and sustainability in each of the worlds. Our results indicate that more equal worlds improve food security over a wider range of food security indicators and neglecting the sustainability dimension might revert food security gains over time. This paper concludes that there is a need for model-based scenario analysis to assess the complex and multi-dimensional characteristics of global food security.