The fingerprint is one of the most popular and used biometric traits for the identification of people, due to its bio-invariant characteristic, precision, and easy acquisition. One of the stages in the identification of fingerprints is classification, this has the objective of reducing the search times and the computational cost in the databases. Currently, there are several academic publications with methods based on convolutional neural networks (CNN) by using fingerprint images as inputs, which have excellent performance in terms of classification; however, these studies have a very high computational cost, and they require high-performance computing, which is not accessible to everyone. This work will be carefully reviewed proposals for fingerprint identifiers and classifiers by employing extreme learning machines (ELM). The methods proposed by the authors will be analyzed, and these will be compared in terms of the overall performance with the different classifiers considered by the authors in their respective works. In this sense, research works with different types of ELM are considered to see the advantages and disadvantages that they present with each other and to verify how they can contribute to reducing the penetration rate of fingerprint databases. The latter is very important since improving the penetration rate implies reducing search times and computational complexity in fingerprint databases.