The paper attempts to highlight the question, if modern complex systems theory can be a relevant and useful tool for agricultural economics and other applied economic disciplines and how. Focus is on the consequences of self-organization, an emergent property of large systems with many components. The proposition is made that economic systems are indeed selforganizing systems and some explorative data analysis, that is a test for power law distributions in the sectors economic changes, is carried out on Danish agricultural sectors, particularly the pork sector. The results suggest that power law distributions exist in the analyzed sectors, which is seen as an indication of self-organization in the sectors under investigation and specifically for "self-organized criticality". If economic systems in fact turn out to be self-organizing, should they not also have similar systems characteristics as other complex systems like attractors, fractal structures, synchronity and other higher emergent system properties? What would be the consequences for the way economic systems, their internal dynamics and external regulation are understood in general economics and particularly in applied economics? The read thread through this paper is an attempt to highlight these questions systematically in a first overview. Then we will turn away from the pork sector example and extend our view to other properties of complex systems and to the "nature" of complex systems in general. Different systems concepts from Boulding´s hierarchy of systems ("clockwork"-, "control"-, "open"-systems) are connected to different economic theories by the question how complexity is dealt with in economic disciplines. Finally ten "lessons learnt" are suggested about how complex systems theory could be made useful in applied economics disciplines and how it could change the way real world economic systems are perceived, analyzed and regulated.