From self-driving vehicles, voice recognition based virtual digital assistants, smart thermostats to recommendation systems, Artificial Intelligence (AI) is becoming a crucial part of the carbon neutral society that has drawn considerable interest from energy supply firms, startups, technology developers, financial institutions, national governments and the academic community. The emergence of AI initiates numerous opportunities to transform energy industry to AI-powered smart system which can revolutionize traditional approaches of creativity thinking, strategical operation, and solution seeking, especially for accelerating carbon neutrality of our society. This survey provides a comprehensive overview of fundamental principles that underpin applications of big data analysis in Energy Internet (EI), such as smart energy supply and consumption, smart health and Fintech. Next, we focus on intelligent decision-making for the energy industry and inform the state-of-the-art by thoroughly reviewing the literature. Subsequently, cybersecurity issues for AI system related to EI are discussed with recent advancements from vulnerability analysis of AI system to differential privacy and to blockchain based security technology. To our knowledge, this is one of the first academic, peer-reviewed works to provide a systematic review of AI applications for EI research and initiatives in terms of big data analysis, intelligent decision-making and AI related cybersecurity These initiatives were systematically classified into different groups according to the field of application, methodology and contribution Afterwards, potential challenges, limitations for existing research and opportunities for future directions are discussed, ranging from emerging explainable AI, to localized multi-energy marketplaces, self-driving electric vehicle charging and e-mobility. This paper can help us understand how to build smart cities and critical infrastructure for a climate-changed world towards the UNâs sustainable development goals.