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Abstract: In the European Union, the building sector is one of the largest energy consumer with about 40% of the final energy consumption. Reducing consumption is also a sociological, technological and scientific matter. New methods have to be devised in order to support building professionals in their effort to optimize designs and to enhance energy performances. Indeed, the research field related to building modelling and energy performances prediction is very productive, involving various scientific domains. Among them, one can distinguish physics-related fields, focusing on the resolution of equations simulating building thermal behaviour and mathematics-related ones, consisting in the implementation of prediction model thanks to machine learning techniques. This paper proposes a detailed review and discussion of these works. First, the approaches based on physical (“white box”) models are reviewed according three-category classification. Then, we present the main machine learning (“black box”) tools used for prediction of energy consumption, heating/cooling demand, indoor temperature. Eventually, a third approach called hybrid (“grey box”) method is introduced, which uses both physical and statistical techniques. The paper covers a wide range of research works, giving the base principles of each technique and numerous illustrative examples. [Copyright &y& Elsevier]