Abstract: The exploration of low-dimensional physics and exotic quantum phenomena require the controlled construction of functional surface nanostructures. The study of these issues is also important for the continuous development of the microelectronic industry. This field includes the novel growth techniques to realize the precise controllability as well as high-resolution characterization of the materials. A proper understanding of the formation dynamics and kinetics promotes optimization of the fabrication methods. Moreover, studying the properties of surface low-dimensional structures in detail can lead to the discovery of new physics and concepts of functional devices. In return, this study will stimulate the development of fundamental research and applications. Here we describe the recent achievements of the State Key Laboratory for Surface Physics in the function design and controlled construction of artificial surface low-dimensional structures.