  Real-world road networks have an approximate scale-invariance property; can
one devise mathematical models of random networks whose distributions are {\em
exactly} invariant under Euclidean scaling? This requires working in the
continuum plane. We introduce an axiomatization of a class of processes we call
{\em scale-invariant random spatial networks}, whose primitives are routes
between each pair of points in the plane. We prove that one concrete model,
based on minimum-time routes in a binary hierarchy of roads with different
speed limits, satisfies the axioms, and note informally that two other
constructions (based on Poisson line processes and on dynamic proximity graphs)
are expected also to satisfy the axioms. We initiate study of structure theory
and summary statistics for general processes in this class.
