Artificial microstructures, which allow us to control and change the properties of wave fields through changing the geometrical parameters and the arrangements of microstructures, have attracted plenty of attentions in the past few decades. Some artificial microstructure based research areas, such as metamaterials, metasurfaces and phononic topological insulators, have seen numerous novel applications and phenomena. The manipulation of different dimensions (phase, amplitude, frequency or polarization) of wave fields, particularly, can be easily achieved at subwavelength scales by metasurfaces. In this review, we focus on the recent developments of wave field manipulations based on artificial microstructures and classify some important applications from the viewpoint of different dimensional manipulations of wave fields. The development tendency of wave field manipulation from single-dimension to multidimensions provides a useful guide for researchers to realize miniaturized and integrated optical and acoustic devices.