The increasing adoption of mobile devices as the preferred tool to access the Internet imposes to deepen the investigation of security aspects. In parallel, their power constrained nature must be explicitly considered in order to analyze security in an effective and comprehensive manner. This aspect, which is often neglected in the literature, allows investigating two important behaviors of mobile devices: (i) evaluate if all the layers accounting for privacy and security can be re-engineered or optimized to save power, and (ii) understand the effectiveness of draining energy to conduct attacks. In this perspective, this paper surveys and highlights the most recent work on energy-awareness and security. Also, it summarizes the current state of the art on general techniques to save energy, as well as tools to perform measurements. The major contributions of this survey are, thus, a review of past work aimed at minimizing the energy footprint of security mechanisms, and the identification of promising research trends, such as detecting attacks via anomalous power consumption.