Pattern classification using neural networks and statistical methods is discussed. We give a tutorial overview in which popular classifiers are grouped into distinct categories according to their underlying mathematical principles; also, we assess what makes a classifier neural. The overview is complemented by two case studies using handwritten digit and phoneme data that test the performance of a number of most typical neural-network and statistical classifiers. Four methods of our own are included: reduced kernel discriminant analysis, the learning k-nearest neighbors classifier, the averaged learning subspace method, and a version of kernel discriminant analysis.