Nanocrystalline materials have been under extensive study in the past two decades. The reduction in grain size induces many abnormal behaviors in the properties of nanocrystalline materials, that have been investigated systematically and quantitatively. As one of the most fundamental relations in materials science, the structure-property relation should still apply on materials of nano-scale grain sizes. The characterization of grain boundaries (GBs) and related entities remains a big obstacle to understanding the structure-property relation in nanocrystalline materials. It is challenging experimentally to determine the topological properties of polycrystalline materials due to the complex and disordered grain boundary network presented in the nanocrystalline materials. The constantly improving computing power enables us to study the structure-property relation in nanocrystalline materials via Monte Carlo and molecular dynamic simulations. In this study, we will first propose a geometrical construction method based on inverse Monte Carlo simulation to generate digital microstructures with desired topological properties such as grain size, interface area, triple junction length as well as their statistical distributions. The influences on the grain shapes by different topological properties are studied. Two empirical geometrical laws are examined including the Lewis rule and Aboav-Weaire law. Secondly, defect free nanocrystalline Copper (nc-Cu) samples are generated by filling atoms into the Voronoi structure and then relaxed by molecular dynamics simulations. Atoms in the relaxed nc-Cu samples are then characterized into grain atoms, GB interface atoms, GB triple junction atoms and vertex atoms using a newly proposed method. Atoms in each GB entity can also be identified. Next, the topological properties of nc-Cu samples before and after relaxation are calculated and compared, indicating that there exists a physical limit in the number of atoms to form a stable grain boundary interface and triple junction in nanocrystalline materials. In addition, we are able to obtain the statistical averages of geometrical and thermal properties of atoms across each GB interfaces, the so-called GB profiles, and study the grain size, misorientation and temperature effects on the microstructures in nanocrystalline materials. Finally, nc-Cu samples with different topological properties are deformed under simple shear using MD simulation in an attempt to study the structure-property relation in nanocrystalline materials.