Abstract: Building a new power system dominated by renewable energy constitutes an inevitable pathway toward building an energy powerhouse. However, the increasing penetration of power electronic devices such as renewable energy units significantly weakens the stability support capability of power systems, and drastically reduces system stability margins. Under these conditions, scarce support resources restrict the adjustable range of stability control as well as active/reactive power scheduling measures, thereby sharply increasing the risk of system instability. To clarify the research lineage of stability support capability planning for new power systems, this paper systematically reviews new power system planning methodologies for enhancing stability support capability. Firstly, the paper analyzes the necessity of coordinated allocation of stability support resources at the planning stage based on the stability mechanisms of frequency, voltage and rotor angle. Secondly, it reviews the key evaluation indices for three categories of stability issues and modeling methods for stability boundaries, and summarizes optimal power system planning models embedded with stability constraints. Thirdly, it outlines prevalent solution algorithms to address the computational challenges introduced by complex stability constraints. Finally, from three perspectives including stability support mechanisms, stability boundary conditions and multi-scale model construction, as well as artificial intelligence-based solution techniques, it discusses the core challenges and prospective research directions in this field.