In this article, we review the representative work that has been done by Hong-Jun Gao's group in the past two decades in Institute of Physics, Chinese Academy of Sciences. The work focuses on the construction, properties and applications of low-dimensional atomic/molecular crystals, covering the following 3 aspects. 1) Construction and growth mechanisms of low-dimensional quantum structures. Firstly, we demonstrate the fabrication and growth mechanism of a seahorse shaped fractal pattern in C60-TCNQ multilayer thin films by using the ionized-cluster-beam method. Secondly, by modifying the tip of the scanning tunneling microscope (STM), we clearly resolve the six rest atoms and twelve adatoms on a Si(111)-77 unit cell, showing the highest-resolution STM images of the Si(111)-77 surface. According to this work, we investigate the adsorption and bonding of Ge atoms on Si(111)-77 at low coverages. The configurations and growth behaviors of iron phthalocyanine molecules on Au(111) surface from sub-monolayer to bilayer are also reviewed. Furthermore, we demonstrate that organic molecules bond preferentially to different facets of the Ag(775) substrate under different deposition sequences, molecular lengths, terrace widths, and step heights. This can contribute to the design of non-templated selective functionalization of nanocrystals. 2) Reversible conductance transition and spin on-off in low-dimensional quantum structures and applications in ultrahigh-density information storage. Firstly, we implement reversible, erasable, and rewritable nano-recordings on molecular thin films as a result of conductance transition. Then we demonstrate that the Kondo resonance of iron phthalocyanine molecules on an Au(111) substrate depends strongly on adsorption configuration, and the Kondo resonance of manganese phthalocyanine molecules can reversibly switch ON and OFF via attachment and detachment of single hydrogen atom to the molecule. Moreover, we achieve the site-dependent g factor of a single magnetic molecule with sub-molecular resolution, which shows an inhomogeneous distribution of the g factor within a single molecule. These results open up new routes to realizing ultrahigh-density information storage and controlling local spin properties within a single molecule. 3) Construction, physical properties and applications of graphene and other two-dimensional atomic crystals. We start with the fabrication of a wafer-size, high-quality (almost defect free), single-crystalline graphene on Ru(0001). Then we demonstrate the structure of novel two-dimensional (2D) atomic crystals of mono-element, such as silicene,germanene, hafnene, and antimonene. Last but not least, we present the formation of intrinsically patterned bi-elements 2D materials, PtSe2 and CuSe, which can serve as templates for selective self-assembly of molecules and nanoclusters, as well as dual functionalization for catalysis or other applications. The series of work done in Hong-Jun Gao's group has laid a solid foundation in the research field of low-dimensional quantum structures and their applications.