As the convenience and cost benefits of Natural User Interface (NUI) technologies are hastening their wide adoption, computing devices equipped with such interfaces are becoming ubiquitous. Used for a broad range of applications, from accessing email and bank accounts to home automation and interacting with a healthcare provider, such devices require, more than ever before, a secure yet convenient user authentication mechanism. This paper introduces a new taxonomy and presents a survey of "point-of-entry" user-device authentication mechanisms that employ a natural user interaction. The taxonomy allows a grouping of the surveyed techniques based on the sensor type used to capture user input, the actuator a user applies during interaction, and the credential type used for authentication. A set of security and usability evaluation criteria are then proposed based on the Bonneau, Herley, Van Oorschot and Stajano framework. An analysis of a selection of techniques and, more importantly, the broader taxonomy elements they belong to, based on these evaluation criteria, are provided. This analysis and taxonomy provide a framework for the comparison of different authentication alternatives given an application and a targeted threat model. Similarly, the taxonomy and analysis also offer insights into possibly unexplored, yet potentially rewarding, research avenues for NUI-based user authentication that could be explored.