Fingerprints have been an invaluable tool for law enforcement and forensics for over a century, motivating research into automated fingerprint-based identification in the early 1960s. More recently, fingerprints have found an application in biometric systems. Biometrics is the automatic identification of an individual based on physiological or behavioural characteristics. Due to its security-related applications and the current world political climate, biometrics is presently the subject of intense research by private and academic institutions. Fingerprints are emerging as the most common and trusted biometric for personal identification. The main objective of this paper is to review the extensive research that has been done on automated fingerprint matching over the last four decades. In particular, the focus is on minutiae-based algorithms. Minutiae features contain most of a fingerprints individuality, and are consequently the most important fingerprint feature for verification systems. Minutiae extraction, matching algorithms, and verification performance are discussed in detail, with open problems and future directions identified.