Continental dynamics，a fundamentalfield of geodynamics，is an important extension of plate tectonics and thus a key research direction in solid Earth sciences. Based on the systematic geological，geophysical and geochemical observations，numerical modeling is an efficientway for studying the processes and mechanism of continental dynamic evolution.This study focuses on the numerical modeling of continental dynamics，with discussion onfour key scientific issues of the continental formation and evolution.① The early Earth geodynamics and the origin of continents.The observed oldest continental crustal rocks have a Hadean age，which means that the continental crust started to form in the very early stage of the Earth.The tectonic regimes of the early Earth are far from well constrained，thatmay include the magma ocean，the heat pipe，the stagnant lid，etc. Thus,it is still an unresolved，cutting-edge geodynamic problem.②Continental lithospheric stability and destruction.The continental lithosphere can experience a long-time evolution of billions of years，during which some cratons keep their general stability，however some others are significantly modified and/or destroyed in the Phanerozoic.Either the long-time-scale stability or the destruction of continental lithosphere is the critical scientific question for furtherstudy.③Continental deep subduction and extreme depth exhumation.The exhumation of ultra-high-pressure (UHP) rock is a typical process representing the material circulation in the subduction channel.The general mode and dynamics arealready understood throughsystematic observations and numerical models. However,the exhumation of super-high pressure rocks from 200~350 km depths challenges the previous models and thus requires further study.④ Continental collision and contrasting mountain building.The deciphering of mountain belt is a key issue of continental dynamics.Sophisticatednumerical models are required for comparison with detailed observations tobetter understand the composite mountain building processes with multiple terranes. In addition，as the most important mountain building process，the first-order driving force of Tibetan plateau evolution is still not well understood，requiring further studies.Based on the discussion of these key scientific issues，future studies incontinental dynamic modeling in two major directions are discussed.The first is problem-driven，requiring new strategies and ideas to solve the above-mentioned key continental dynamic problems，especially the first-order mechanisms.The second direction is technique- driven，which calls for the new numerical modeling methods and technologies，e.g.two-phase flow or even multi-phase flow，to meet the requirements of complex geological processes，for example，the phase change，the aqueous fluid flow，the magmatism and the surficial processes.The progresses of both directions are going to improve the understanding of continental dynamicsand further promote the development of continental dynamics theory.