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The computation of sound transmission through solid structures has been of great interest since the first half of the 20th century. Several prediction methods can be found in the large body of literature, applicable to many kinds of structures, and derived using different approaches. This article presents a review of the most significant approaches to compute sound transmission through a building partition; it aims to provide an extensive update and critical literature review of the different approaches which can be used to compute sound transmission through a building partition. Different approaches, suitable for different kinds of building structures, based on analytical and semi-analytical solutions, wave-propagation, numerical or statistical energy analysis methods are described, highlighting advantages and drawbacks.