Novel food technologies are important for food security, safety and sustainability. Consumers, however, are often hesitant to accept them. In this narrative Review, we organize the research describing how heuristics and individual differences among consumers influence the acceptance of agri-food technologies. Associations evoked by a food technology, its perceived naturalness and trust in the industry using it influence consumer acceptance. Food neophobia, disgust sensitivity and cultural values are crucial personality factors for explaining individual differences. Using gene technology, nanotechnology, cultured meat and food irradiation as cases, we explore factors that may explain consumers' acceptance or lack of acceptance. Climate change, food supply shocks caused by crises such as pandemics and population growth are imminent threats to the food system. Therefore, disruptive food technologies will be needed to progress towards a more resilient food system. Taking into account the factors influencing consumers' perceptions of novel food technologies during the early stage of development and introduction will hopefully result in a higher acceptance of such technologies. Consumer acceptance of novel and disruptive technologies is key to their implementation and to building capacity for transforming food systems. Using gene technology, nanotechnology, cultured meat and food irradiation as cases, this Review explores consumer acceptance through the frames of food neophobia, disgust sensitivity and cultural values.