The permeability of porous media wall enhances the momentum and energy transport near the interface, leading to the increase of complexity of flow in the turbulent boundary layer over porous media wall. The porous media wall affects the space-time evolution of turbulent structure directly, generation mechanism and transport characteristics of various physical quantities in the turbulent boundary layer. This paper summarizes the state of the art of statistical and turbulent structure characteristics of boundary layers over porous media wall. Firstly, the properties of porous media substrates have a direct relationship with turbulent boundary layer characteristics, as demonstrated by mean statistical quantum, the wall friction coefficient and characteristics of coherent structures. The structure characteristics of turbulent in the turbulent boundary layer over porous walls are closely related to the Kelvin-Helmholtz (KH) instability induced by porous media. Secondly, the paper discusses the modulation effect of large-scale turbulent structures on small-scale turbulent structures near wall region in porous wall boundary layers. Finally, we outline future research directions.