Metamaterial and photonic crystal concepts are explored throughout and applied to the design of meta-arrays and metasurfaces for new avenues of wave propagation control, across a variety of wave regimes. Numerical tools are developed for characterising the dispersive properties of line arrays of mass-loaded Kirchhoff-Love elastic plates, which are used to design adiabatically graded arrays capable of exhibiting mode conversion and rainbow effects; important distinctions between the spatially selective, by frequency, trapping and reflection phenomena motivate uses for each in terms of energy harvesting and reversed mode conversion respectively. Limitations of slowly varying media are then relaxed, with similar phenomena shown for abrupt transition regions along the array by incorporating crystal momentum transfer. These devices, applied across electromagnetism and underwater acoustics, then emulate negative refraction along a line and subsequently form flat Umklapp lenses and transducers. The effects at an abrupt transition region are then amalgamated with the adiabatic structures in the setting of vector elasticity, forming a device capable of tailored surface to body wave conversion.