In the face of climate change, rising hunger and mass extinctions, scholars stress the need to transition food systems from fossil fuel-dependent conventional farms to agroecological alternatives that can store carbon, improve food security and harbor biodiversity. Theory provides a systematic approach for organizing knowledge on agroecological transitions across the natural and social sciences and summarizing the primary needs of future research. This paper reviews the socio-ecological literature related to agroecological transitions from a mathematical perspective that is derived from complex systems and critical transition theory. We organize the literature according to mathematically tractable concepts, including syndromes of production, agents, barriers and drivers of change that operate across three major frameworks of analysis: socio-ecological, socio-technological and social norms and networks. Our approach embeds the current agroecological transition theory within a critical transition framework that considers the stability of peasant and capitalist syndromes in response to various inhibitors and drivers of change. We find that the majority of our theoretical knowledge of food systems change is derived from the social sciences and limited primarily to examples from the Americas. Our work suggests a need for broader regional representations of change and transdisciplinary work aimed at better understanding how biophysical factors collide with socio-political conditions to hinder or reverse food systems change. Though scale and context are important considerations, we find that theory can generate general mechanisms that link separate case studies. For example, drivers of food systems change that shift balances between the costs and benefits of peasant and capitalist modes of production may be particularly important for explaining poverty and gilded traps in agriculture. We discuss this and other lessons learned from taking a theoretical perspective on agroecological transitions.