Abstract: Abstract: In this talk, I will mainly present our recent studies on the inner structure of early-type galaxies, which provide unique tests for the predictions of the cold dark matter cosmology and the baryonic physics assumptions entering models for galaxy formation. Using the state-of-the-art Illustris simulation, we studied the correlations of three main properties of early-type galaxies, namely, the stellar orbital anisotropies, the central dark matter fractions and the central radial density slopes, as well as their redshift evolution since z  = 1.0. A self-consistent picture was observed and to be tested by existing and future observations, that lower-mass galaxies or galaxies at higher redshift tend to be bluer in rest-frame colour, have higher central gas fractions, and feature more tangentially anisotropic orbits and steeper central density slopes than their higher-mass or lower-redshift counterparts, respectively. Among them, the stellar orbital distribution is of particular interest, as it provides crucial information about the assembly history during galaxy formation. In addition, it also provides a crucial piece of information in galaxy modelling process, without which, commonly used modelling techniques could result in biased determination on galaxy mass distribution. By comparisons between simulations and existing observations, potential challenges to the stellar formation and feedback models adopted by simulations were also unveiled.