  An effective surface equation, that encapsulates the detail of a
microstructure, is developed to model microstructured surfaces. The equations
deduced accurately reproduce a key feature of surface wave phenomena, created
by periodic geometry, that are commonly called Rayleigh-Bloch waves, but which
also go under other names such as Spoof Surface Plasmon Polaritons in
photonics. Several illustrative examples are considered and it is shown that
the theory extends to similar waves that propagate along gratings. Line source
excitation is considered and an implicit long-scale wavelength is identified
and compared to full numerical simulations. We also investigate non-periodic
situations where a long-scale geometric variation in the structure is
introduced and show that localised defect states emerge which the asymptotic
theory explains.
