Chapter 3 starts with a brief discussion how theoretical currents have shaped the distribution of governmental functions between levels of the state, looking at clusters of functions which in OECD countries (but also elsewhere) sit with the national and subnational level, respectively. We conclude that mimicking a particular distribution of functions in the context of a decentralization reform will not help much, and that engaging in a functional assignment process as described here is a more promising approach. We present and describe at some length different types of vertical relationships between the national/central and subnational level as influenced by the particular modality of decentralization that has been chosen (i.e. deconcentration, delegation or devolution). We elaborate particularly two broad models of a functional assignment architecture, i.e. the general competence model (sometimes also called ‘general mandate model’) and the ‘positive/negative list model’, two archetypes of a functional assignment architecture that we found helpful in our country experiences. Finally, we introduce here several typologies of functions, like exclusive, reserved and concurrent functions, obligatory vs optional functions, and residual functions. Having a clear understanding of these typologies and how to use them in functional assignment processes will provide much clarity to the stakeholders involved in these processes and help steer the process in the direction of a stable and workable arrangement.