This paper presents an overview of the literature on privacy protection in smart meters with a particular focus on Homomorphic Encryption (HE). Firstly, we introduce the concept of smart meters, the context in which they are inserted, the main concerns, and oppositions inherent to their use. Later,}an overview of privacy protection is presented, emphasizing the need to safeguard the privacy of smart-meter users by identifying, describing, and comparing the main approaches that seek to address this problem. Then, two privacy protection approaches based on HE are presented in more detail and additionally we present two possible application scenarios. Finally, the paper concludes with a brief overview of the unsolved challenges in HE and the most promising future research directions.