Energy consumption forecasting is essential for efficient resource management related to both economic and environmental benefits. Forecasting can be implemented through statistical analysis of historical data, application of Artificial Intelligence (AI) algorithms, physical models, and more, and focuses on two directions: the required load for a specific area, e.g., a city, and the required load for a building. Building power forecasting is challenging due to the frequent fluctuation of the required electricity and the complexity and alterability of each building’s energy behavior. This paper focuses on the application of Deep Learning (DL) methods to accurately predict building (residential, commercial, or multiple) power consumption, by utilizing the available historical big data. Research findings are compared to state-of-the-art statistical models and AI methods of the literature to comparatively evaluate their efficiency and justify their future application. The aim of this work is to review up-to-date proposed DL approaches, to highlight the current research status, and to point out emerging challenges and future potential directions. Research revealed a higher interest in residential building load forecasting covering 47.5% of the related literature from 2016 up to date, focusing on short-term forecasting horizon in 55% of the referenced papers. The latter was attributed to the lack of available public datasets for experimentation in different building types, since it was found that in the 48.2% of the related literature, the same historical data regarding residential buildings load consumption was used.