The refraction and reflection are basic phenomena in the propagation of all kinds of waves, such as light waves, electromagnetic waves and acoustic waves, when they encounter the interface between different kinds of materials. Recently, it is discovered that the traditional optical laws regarding refraction and reflection can be rewritten when artificially designed subwavelength arrays are fabricated on the interfaces. The revised laws provide promising alternatives to achieve imaging, multi-physics decoupling and holographic display. Here we review the recent progresses in this emerging topic, including the refraction and reflection behavior in various materials configurations, the fundamental theories and practical applications. Finally, based on our recent results, the shortcomings of current researches are analyzed with a look towards the future trends of the overall area.