Traditionally, anatomical and physiological descriptions of hemispheric specialization have focused on hemispheric asymmetries of local brain structure or local functional properties, respectively. This article reviews the current state of an alternative approach that aims at unraveling the causes and functional principles of hemispheric specialization in terms of asymmetries in connectivity. Starting with an overview of the historical origins of the concept of lateralization, we briefly review recent evidence from anatomical and developmental studies that asymmetries in structural connectivity may be a critical factor shaping hemispheric specialization. These differences in anatomical connectivity, which are found both at the intra- and inter-regional level, are likely to form the structural substrate of different functional principles of information processing in the two hemispheres. The main goal of this article is to describe how these functional principles can be characterized using functional neuroimaging in combination with models of functional and effective connectivity. We discuss the methodology of established models of connectivity which are applicable to data from positron emission tomography and functional magnetic resonance imaging and review published studies that have applied these approaches to characterize asymmetries of connectivity during lateralized tasks. Adopting a model-based approach enables functional imaging to proceed from mere descriptions of asymmetric activation patterns to mechanistic accounts of how these asymmetries are caused.