The projected human population of nine billion by 2050 has led to ever growing discussion of the need for increasing agricultural output to meet estimated food demands, while mitigating environmental costs. Many stakeholders in agricultural circles are calling for the intensification of agriculture to meet these demands. However, it is neither clear nor readily agreed upon what is meant by intensification. Here, we compare the three major uses, 'ecological intensification', 'sustainable intensification' and 'agroecological intensification', by analysing their various definitions, principles and practices, and also their historical appearance and evolution. We used data from the scientific literature, the grey literature, the websites of international organizations and the Scopus and FAOLEX databases. Our major findings are: (1) sustainable intensification is the most frequently used term so far. (2) The three concepts ecological intensification, sustainable intensification and agroecological intensification overlap in terms of definitions, principles and practices, thus creating some confusion in their meanings, interpretations and implications. Nevertheless, some differences exist. (3) Sustainable intensification is more widely used and represents in many cases a rather generalised category, into which most current farming practices can be put so long as sustainability is in some way addressed. However, despite its wider use, it remains imprecisely defined. (4) Ecological and agroecological intensification do introduce some major nuances and, in general, more explicitly stated definitions. For instance, ecological intensification emphasizes the understanding and intensification of biological and ecological processes and functions in agroecosystem. (5) The notion of agroecological intensification accentuates the system approach and integrates more cultural and social perspectives in its concept. (6) Even if some boundaries can be seen, confusion is still predominant in the use of these terms. These blurred boundaries currently contribute to the use of these terms for justifying many different kinds of practices and interventions. We suggest that greater precision in defining the terms and the respective practices proposed would indicate more clearly what authors or institutions are aiming at with the proposed intensification. In this sense, we provide new definitions for all three intensification concepts based on the earlier ones.