Enormous amounts of data are being produced everyday by submeters and smart sensors installed in different kinds of buildings. If leveraged properly, that data could assist end-users, energy producers and utility companies in detecting anomalous power consumption and understanding the causes of each anomaly. Therefore, anomaly detection could stop a minor problem to become widespread, costly and time-consuming issue. Moreover, this will help in better decision-making to reduce wasted energy and promote sustainable and energy efficiency behavior. In this regard, this paper is proposed to indepthly review existing frameworks of anomaly detection in power consumption and provide a critical analysis of existing solutions. Specifically, a comprehensive survey is introduced, in which a novel taxonomy is introduced to classify existing algorithms based on different factors adopted in their implementation, such as the machine learning algorithm, feature extraction approach, detection level, computing platform, application scenario and privacy preservation. To the best of the authors' knowledge, this is the first review article that discusses the anomaly detection in building energy consumption. Moving forward, important findings along with domain-specific problems, difficulties and challenges that remain unresolved are thoroughly discussed, including the absence of: (i) precise definitions of anomalous power consumptions, (ii) annotated datasets, (iii) unified metrics to assess the performance of existing solutions, and (iv) platforms for reproducibility. Following, insights about current research trends that anomaly detection technology needs to target for widespreading its application and facilitate its implementation are described before deriving a set of challenging future directions attracting significant research and development attention.