Advanced metering infrastructure (AMI) enables real-time collection of power consumption data through the Smart Grid communication network. With the current deployment of smart meters (SMs), one of the concerns that started to be raised by the customers is on the privacy of their power consumption data. The exposure of these data can lead to several privacy problems that need to be addressed before the customers can be convinced for the use of SMs. This paper has two contributions. First, it identifies the threats regarding user and data privacy in AMI applications and comprehensively surveys the existing solutions to address these threats. We categorize the existing approaches on privacy and discuss pros and cons of these approaches with respect to some criteria. Second, we pick one of the existing solutions on privacy, namely the homomorphic encryption, and evaluate its feasibility and impact on performance when used in data aggregation for real-time AMI applications. We investigate and compare the performance of homomorphic encryption in terms of data size and end-to-end delay with that of hop-by-hop secure data aggregation and data concatenation within a network of SMs via extensive simulations. We finally conclude the paper with some future privacy issues that are subject to further research. Copyright © 2013 John Wiley & Sons, Ltd.