The technological development of smart grids (SGs) has recently gained increased momentum due to large-scale integration of renewable energy sources (e.g., wind and photovoltaic power) and highly variable loads, including electric vehicles (EVs) along with the deepened decarbonization in power and transport systems as two major greenhouse gas-emitting sectors worldwide. With the development of SGs, fruitful achievements in optimal scheduling and distributed cooperative control have been made. However, a comprehensive survey of these methods covering the low-carbon, economy, and cybersecurity metrics is still missing. This paper bridges the gap with the aim of providing an in-depth overview of optimal scheduling and distributed cooperative control from the whole system perspective within the SG framework. First, the fundamental mathematical models of optimal scheduling for low-carbon, economy, and cybersecurity operations are reviewed, the corresponding solution methods are summarized, and the cooperative optimization and scheduling methods for SGs integrated with EVs are specifically analyzed. Second, the performances of centralized and distributed cooperative control methods are compared, and two popular distributed cooperative control frameworks, namely centralized-distributed and autonomous-distribute frameworks, are further discussed comprehensively. Third, typical real-world applications of optimal scheduling and distributed cooperative control are analyzed. Finally, the trends and challenges of optimal scheduling and distributed cooperative control for effectively integrating EVs in SGs are prospected.