Organizational ambidexterity has emerged as a new research paradigm in organization theory, yet several issues fundamental to this debate remain controversial. We explore four central tensions here: Should organizations achieve ambidexterity through differentiation or through integration? Does ambidexterity occur at the individual or organizational level? Must organizations take a static or dynamic perspective on ambidexterity? Finally, can ambidexterity arise internally, or do firms have to externalize some processes? We provide an overview of the seven articles included in this special issue and suggest several avenues for future research.