The paper studies Support Vector Machines (SVMs) in the context of face verification and recognition. Our study supports the hypothesis that the SVM approach is able to extract the relevant discriminatory information from the training data and we present results showing superior performance in comparison with benchmark methods. However, when the representation space already captures and emphasizes the discriminatory information (e.g. Fisher's linear discriminant), SVMs loose their superiority. The results also indicate that the SVMs are robust against changes in illumination provided these are adequately represented in the training data. The proposed system is evaluated on a large database of 295 people obtaining highly competitive results: an equal error rate of 1% for verification and a rank-one error rate of 2% for recognition (or 98% correct rank-one recognition).