Abstract: Nanosystems play an important role in many applications. Due to their complexity, it is challenging to accurately characterize their structure and properties. An important means to reach such a goal is computational simulation, which is grounded on ab initio electronic structure calculations. Low scaling and accurate electronic-structure algorithms have been developed in recent years. Especially, the efficiency of hybrid density functional calculations for periodic systems has been significantly improved. With electronic structure information, simulation methods can be developed to directly obtain experimentally comparable data. For example, scanning tunneling microscopy images can be effectively simulated with advanced algorithms. When the system we are interested in is strongly coupled to environment, such as the Kondo effect, solving the hierarchical equations of motion turns out to be an effective way of computational characterization. Furthermore, the first principles simulation on the excited state dynamics rapidly emerges in recent years, and nonadiabatic molecular dynamics method plays an important role. For nanosystem involved chemical processes, such as graphene growth, multiscale simulation methods should be developed to characterize their atomic details. In this review, we review some recent progresses in methodology development for computational characterization of nanosystems. Advanced algorithms and software are essential for us to better understand of the nanoworld.