Dyakonov surface waves (DSWs) are surface electromagnetic waves that travel along the interface in between an isotropic and an uniaxial-birefringent medium. They were theoretically predicted in 1988 by the Russian physicist Mikhail Dyakonov. Unlike other types of acoustic and electromagnetic surface waves, the DSW's existence is due to the difference in symmetry of materials forming the interface. He considered the interface between an isotropic transmitting medium and an anisotropic uniaxial crystal, and showed that under certain conditions waves localized at the interface should exist. Later, similar waves were predicted to exist at the interface between two identical uniaxial crystals with different orientations.
The previously known electromagnetic surface waves, surface plasmons and surface plasmon polaritons, exist under the condition that the permittivity of one of the materials forming the interface is negative, while the other one is positive (for example, this is the case for the air/metal interface below the plasma frequency).  In contrast, the DSW can propagate when both materials are transparent; hence they are virtually lossless, which is their most fascinating property.
In recent years, the significance and potential of the DSW have attracted the attention of many researchers: a change of the constitutive properties of one or both of the two partnering materials – due to, say, infiltration by any chemical or biological agent – could measurably change the characteristics of the wave. Consequently, numerous potential applications are envisaged, including devices for integrated optics, chemical and biological surface sensing, etc.
However, it is not easy to satisfy the necessary conditions for the DSW, and because of this the first proof-of-principle experimental observation of DSW 
was reported only 20 years after the original prediction.
A large number of theoretical work appeared dealing with various aspects of this phenomenon, see the detailed review. In particular, DSW propagation at magnetic interfaces, in left-handed materials, in electro-optical, and chiral materials was studied. Resonant transmission due to DSW in structures using prisms was predicted, and combination and interaction between DSW and surface plasmons (Dyakonov plasmons) was studied and observed.