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There are three main approaches to reconstructing quantitatively Holocene environments from fossil biological assemblages:(1) indicator species,(2) assemblage or modern analogues (including response surfaces) and (3) multivariate transfer functions. Their assumptions, strengths and limitations are discussed. The basic concepts, requirements and numerical procedures involved in transfer functions are reviewed, and the properties of weighted averaging and weighted averaging partial least squares regression are outlined. A reconstruction of Holocene mean July temperatures in northern Norway from pollen-stratigraphical data is presented. Possible future developments are discussed.