In this paper, we study the properties of routing functions in non-timed Petri nets with respect to the nets' semantics. We consider two types of routing (origin dependent and origin independent) which are not mutually representable, and describe the net semantics induced. For unequivocal routing, the process behavior - definable only in the origin dependent case - is shown to be unique up to isomorphism. We show that every routed net is weakly routing place bisimilar to a Free Choice net. This fact, in turn, facilitates the subsequent study of fairness properties, which are characterized by the local equitability of the routing functions.