The Smart grid (SG), generally known as the next-generation power grid emerged as a replacement for ill-suited power systems in the 21st century. It is in-tegrated with advanced communication and computing capabilities, thus it is ex-pected to enhance the reliability and the efficiency of energy distribution with minimum effects. With the massive infrastructure it holds and the underlying communication network in the system, it introduced a large volume of data that demands various techniques for proper analysis and decision making. Big data analytics, machine learning (ML), and deep learning (DL) plays a key role when it comes to the analysis of this massive amount of data and generation of valuable insights. This paper explores and surveys the Smart grid architectural elements, machine learning, and deep learning-based applications and approaches in the context of the Smart grid. In addition in terms of machine learning-based data an-alytics, this paper highlights the limitations of the current research and highlights future directions as well.