Power systems around the world are being modernized to address environmental concerns, reduce costs, and guarantee access to electricity all the time. Four main criteria for this upgrade are efficiency, reliability, resiliency and sustainability. Recent advances in various technologies are the key enablers for this modernization. Nevertheless, such physical systems are becoming overwhelmingly large-scale and stochastic with highly complex dynamics, coupled with millions of human interactions. The design and operation of these systems needs major innovations in computational techniques. In this talk, we first discuss some major challenges behind the modernization of power grids and explain why addressing them involves many different fields. Then, we focus on three topics of optimization, learning, and control for power systems, which all need major revolutions in computational techniques. We study how recent advances in AI and machine learning can assist with addressing some of these challenges. We offer case studies on the grids for California, Texas, and different parts of Europe.