The need to feed nine billion people in 2050 has given rise to widespread debate in science and policy circles. The debate is largely framed in neo-Malthusian terms, and elements of global food security (resilience of the food system, food quantity and quality, right to and access to food) demand equal attention. High-intensive agriculture, which enabled population growth and food for a large proportion of the global population, is often regarded as incompatible with current environmental (and social) sustainability. Because of the often problematic nature of high-intensive industrialized agriculture, sustainable agricultural intensification has been called an oxymoron. Pathways to sustainably intensify agriculture vary from business-as-usual to claims that a radical rethinking of our agricultural production is imperative. Three terms have been coined to differentiate such pathways. Whereas conventional intensification, that is business-as-usual, is uncontroversial (but often considered unlikely to be able to achieve environmental sustainability), the phrases sustainable intensification and ecological intensification both have a complex history. Although one could think that they have similar meanings, the phrases represent very different perspectives in discourses in science and policy circles. The terms Utopians and Arcadians are introduced for adherents of those perspectives. We observe that they both devote insufficient attention to inevitable trade-offs. Agricultural intensification in developing countries was greatly accelerated by the Green Revolution, which largely bypassed sub-Saharan Africa. Discontent with that outcome has led to a plethora of new terms to indicate more successful next steps for sub-Saharan agriculture. Industrialized agriculture as currently practised in developed countries will not provide a universal solution. This epilogue of the special issue and the literature herein show that intense debates on sustainable agricultural intensification are needed. Such debates on intensification demand reflection on the role of scientists with regard to their uses of current and the generation of novel knowledge.