The energy internet (EI) integrated with smart grid (SG) has been a growing and emerging technology that manages and controls towards reliability, security, data integrity, demand response management, cyber-attacks, efficient utility energy service, and protocols. Nevertheless, EI-based SG implementation has several shortcomings, such as scalability, congestion, and pricing, making the entire system vulnerable and complex. Hence, this paper comprehensively reviews the EI concept for utility energy service and demand-side management (DSM) in SG, related issues, and future directions. In line with the matter, this review showcases an inclusive description of EI technology, highlighting architecture, theory, and applications. Besides, the various EI integrated utility services are discussed with regard to cloud-based utility service, one-stop online utility service, short message service-based utility service, future utility service, and affordable utility service. Moreover, the DSM in SG connected with EI environment is explored, covering the resilience of EI architecture, 5G based EI, and EI-based DSM for sustainable consumption. The numerous key issues, problems, and challenges are outlined to identify the existing research gaps. Finally, the review proposes some improvements for future opportunities and developments for EI in utility energy service and DSM in SG. All the critical discussion, analysis, and suggestions would be valuable for the power engineer and researchers to enhance EI-based SG for future sustainable operation and management.