  In many physical situations involving diverse length scales, waves or rays
representing them travel through media characterized by spatially smooth,
random, modest refactive index variations. "Primary" diffraction (by individual
sub-wavelength features) is absent. Eventually the weak refraction leads to
imperfect focal "cusps". Much later, a statistical regime characterized by
momentum diffusion is manifested. An important intermediate regime is often
overlooked, one that is diffusive only in an ensemble sense. Each realization
of the ensemble possesses dramatic ray limit structure that guides the waves
(in the same sense that ray optics is used to design lens systems). This
structure is a universal phenomenon called branched flow. Many important
phenomena develop in this intermediate regime. Here we give examples and some
of the physics of this emerging field.
