In this article, we review and discuss algorithms for adaptive data-driven soft sensing. In order to be able to provide a comprehensive overview of the adaptation techniques, adaptive soft sensing methods are reviewed from the perspective of machine learning theory for adaptive learning systems. In particular, the concept drift theory is exploited to classify the algorithms into three different types, which are: (i) moving windows techniques; (ii) recursive adaptation techniques; and (iii) ensemble-based methods. The most significant algorithms are described in some detail and critically reviewed in this work. We also provide a comprehensive list of publications where adaptive soft sensors were proposed and applied to practical problems. Furthermore in order to enable the comparison of different methods to standard soft sensor applications, a list of publicly available data sets for the development of data-driven soft sensors is presented. (C) 2010 Elsevier Ltd. All rights reserved.