A power curve relates the power produced by a wind turbine to the wind speed. Usually, such curves are unique to the various types of wind turbines, so that by monitoring the power curves, one may monitor the performance of the turbine itself. Most approaches to monitoring a system or a structure at a basic level, generally aim at differentiating between a normal and an abnormal state. Typically, the normal state is represented by a model, and then abnormal, or extreme data points are identified when they are compared to that model. This comparison is very often done pointwise on scalars in the univariate case, or on vectors, if multivariate features are available. Depending on the actual application, the pointwise approach may be limited, or highly prone to false identifications. This paper presents the use of extreme functions for the performance monitoring of wind turbines. Power curves from an actual wind turbine, are assessed as whole functions, and not individual datapoints, with the help of Gaussian process regression and extreme value distributions, with the ultimate aim of the performance monitoring of the wind turbine at a weekly resolution. The approach is compared to the more conventional pointwise method, and approaches which make use of multivariate features, and is shown to be superior in terms of the number of false identifications, with a significantly lower number of false-positives without sacrificing the sensitivity of the approach. (C) 2017 The Authors. Published by Elsevier Ltd.