Touchless fingerprint recognition represents a rapidly growing field of research which has been studied for more than a decade. Through a touchless acquisition process, many issues of touch-based systems are circumvented, e.g., the presence of latent fingerprints or distortions caused by pressing fingers on a sensor surface. However, touchless fingerprint recognition systems reveal new challenges. In particular, a reliable detection and focusing of a presented finger as well as an appropriate preprocessing of the acquired finger image represent the most crucial tasks. Also, further issues, e.g., interoperability between touchless and touch-based fingerprints or presentation attack detection, are currently investigated by different research groups. Many works have been proposed so far to put touchless fingerprint recognition into practice. Published approaches range from self identification scenarios with commodity devices, e.g., smartphones, to high performance on-the-move deployments paving the way for new fingerprint recognition application scenarios.This work summarizes the state-of-the-art in the field of touchless 2D fingerprint recognition at each stage of the recognition process. Additionally, technical considerations and trade-offs of the presented methods are discussed along with open issues and challenges. An overview of available research resources completes the work.