The traditional electrical grid has to be digitally improved as digitalization and effective integration of renewable energy bring better efficiency, intelligence, and safety into the grid; hence, the transition from the traditional grid to a smart grid. A smart grid is a modernized and digitalized standard electrical infrastructure that has a key component known as the advanced metering infrastructure (AMI). AMI, also known as smart metering, is a key technological enabler of the smart grid that allows automatic collection and reporting of power-consumed data via two-way communication networks. However, the collected power consumption data is confidential; hence, its privacy must be maintained. Similarly, for the benefit of the smart grid to be consistently maximized, the AMI data and network security must always be intact despite the evolving threats and attacks targeted at it.This paper provides a comprehensive review of the existing vulnerabilities/attacks, security and privacy challenges associated with the smart metering data and network system, its open issues, and future direction. The major contributions of this review paper lie in the AMI vulnerabilities, AMI state-of-the-art security schemes with their pros and cons, its communication protocols analysis, and its emerging security measures. This gave enumerated recommendations for the efficiency improvement of AMI security in terms of its latency reduction while implementing efficient security measures in its future work.