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In recent years, many nearest neighbor algorithms based on fuzzy sets theory have been developed. These methods form a field, known as fuzzy nearest neighbor classification, which is the source of many proposals for the enhancement of the k nearest neighbor classifier. Fuzzy sets theory and several extensions, including fuzzy rough sets, intuitionistic fuzzy sets, type-2 fuzzy sets and possibilistic theory are the foundations of these hybrid techniques, designed to tackle some of the drawbacks of the nearest neighbor rule. In this paper the most relevant approaches to fuzzy nearest neighbor classification are reviewed, as are applications and theoretical works. Several descriptive properties are defined to build a full taxonomy, which should be useful as a future reference for new developments. An experimental framework, including implementations of the methods, datasets, and a suggestion of a statistical methodology for results assessment is provided. A case of study is included, featuring a comparison of the best techniques with several state of the art crisp nearest neighbor classifiers. The work concludes with the suggestion of some open challenges and ways to improve fuzzy nearest neighbor classification as a machine learning technique.