Laminar-turbulent transition prediction in hypersonic boundary layer remains one of the most challenging topics in the design of hypervelocity vehicle. It requires thorough understanding of the physical mechanisms underlay freestream wave receptivity and nonlinear breakdown process. Freestream wave receptivity concerns the evolution of freestream disturbance passing through the shock and exciting the boundary layer normal modes that eventually become unstable. Nonlinear breakdown focuses on the study of the relevant mechanisms in the secondary instability region that leads to laminar-turbulent transition. These two topics have been extensively studied separately for decades. Significant progress has been made in terms of understanding how the instability waves form and develop in the early region as well as what are the viable paths from breakdown to turbulent. However, the linkage between receptivity and breakdown is still not well understood. The nature transition process commonly observed in hypersonic boundary layer consists of the following ingredients: freestream wave receptivity, linear growth, secondary instability and breakdown to turbulent. The transition location highly depends on the freestream wave disturbance profile. In order to attain a better understanding of the natural transition process, it is necessary to conduct a complete simulation from freestream wave receptivity all the way to nonlinear breakdown. This kind of simulation is considered beyond the capability of current computer power. The objective of current research is to devise a new three-step approach to simulate the flow from receptivity process to breakdown. In order to achieve the goal, direct numerical simulations (DNS) are performed over various freestream conditions and cone geometries to investigate the hypersonic boundary layer stability, freestream wave receptivity and nonlinear breakdown. In the study of nose bluntness effect on hypersonic boundary layer stability, three cone models with different nose radii are investigated by linear stability theory (LST). It is found that, if only considering the second-mode instabilities, the onset of instability is always delayed as the nose bluntness increases. In the effort to simulate the entire process from freestream wave receptivity to nonlinear breakdown, a new approach is applied to break the simulation into three steps: meanflow calculation, linear receptivity simulation and nonlinear breakdown simulation. Extensive case studies demonstrate that it is feasible to simulate the flow from receptivity to breakdown using our new simulation approach. From the breakdown simulations, it is found that the breakdown is the result of fundamental resonance that occurs between the two-dimensional second-mode wave and their three-dimensional modes. In the secondary instability growth region, the two-dimensional and three-dimensional modes need to attain the same amplitude level for the breakdown to take place.