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The widespread adoption of the fifth generation (5G) of cellular networks has brought new opportunities for localization-based services. High-precision positioning use cases and functionalities defined by the standards are drawing the interest of vertical industries. In the transition to the deployment, this paper aims to provide an in-depth tutorial on 5G positioning, summarizing the historical events that led to the standardization of cellular-based positioning, describing current and forthcoming releases of the Third Generation Partnership Project (3GPP) standard, and discussing about the major research trends. This paper is intended to represent an exhaustive guide for researchers and practitioners by providing fundamental notions on wireless localization, comprehensive definitions of measurements and architectures, examples of algorithms, and details on simulation approaches. Our approach aims to merge practical aspects of enabled use cases and related requirements with theoretical methodologies and fundamental bounds, allowing to understand the trade-off between system complexity and achievable, i.e., tangible, benefits of 5G positioning services. We also discuss about current limitations to be resolved for delivering accurate positioning solutions. We evaluate the performances of 3GPP Rel-16 positioning in outdoor and indoor environments, providing thorough analyses of the effect of changing the system configuration.