The attainment of carbon neutrality requires a research agenda that addresses the technical and economic challenges that will be encountered as we progress toward 100% renewable electricity generation. Increasing proportions of variable renewable energy (VRE) sources (such as wind turbines and photovoltaic systems) render the supply-and-demand balance of VRE-dominated power grids difficult. The operational characteristics and effects of VRE inverters also require attention. Here, we examine the implications of the paradigm shift to carbon neutrality and summarize the associated research challenges in terms of system planning, operation, and stability, and the need for energy storage integration, demand-side participation, distributed control and estimation, and energy sector coupling. We also highlight the existing literature gaps, and our recent studies that can fill in the gaps, thereby facilitating the improvement of grid operation and estimation. The numerical results of comparative case studies are also provided on the operational stability and economics of power grids with a high level of VRE sources, assisting stakeholders in establishing specific roadmaps and making relevant decisions.