Advanced Metering Infrastructure (AMI) is a component of electrical networks that combines the energy and telecommunication infrastructure to collect, measure and analyze consumer energy consumptions. One of the main elements of AMI is a smart meter that used to manage electricity generation and distribution to end-user. The rapid implementation of AMI raises the need to deliver better maintenance performance and monitoring more efficiently while keeping consumers informed on their consumption habits. The convergence from analog to digital has made AMI tend to inherit the current vulnerabilities of digital devices that prone to cyber-attack, where attackers can manipulate the consumer energy consumption for their benefit. A huge amount of data generated in AMI allows attackers to manipulate the consumer energy consumption to their benefit once they manage to hack into the AMI environment. Anomalies detection is a technique can be used to identify any rare event such as data manipulation that happens in AMI based on the data collected from the smart meter. The purpose of this study is to review existing studies on anomalies techniques used to detect data manipulation in AMI and smart grid systems. Furthermore, several measurement methods and approaches used by existing studies will be addressed.