This paper presents a detailed analysis of big data and machine learning (ML) in the electrical power and energy sector. Big data analytics for smart energy operations, applications, impact, measurement and control, and challenges are presented in this paper. Big data and machine learning approaches need to be applied after analyzing the power system problem carefully. Determining the match between the strengths of big data and machine learning for solving the power system problem is of utmost important. They can be of great help to plan and operate the traditional grid/smart grid (SG). The basics of big data and machine learning are described in detailed manner along with their applications in various fields such as electrical power and energy, health care and life sciences, government, telecommunications, web and digital media, retailers, finance, e-commerce and customer service, etc. Finally, the challenges and opportunities of big data and machine learning are presented in this paper.