The widespread adoption of the fifth generation (5G) of cellular networks has brought new opportunities for the development of localization-based services. High-accuracy positioning use cases and functionalities defined by the standards are drawing the interest of vertical industries. In the transition towards the deployment, this paper aims to provide an in-depth tutorial on 5G positioning, summarizing the evolutionary path that led to the standardization of cellular-based positioning, describing the localization elements in current and forthcoming releases of the Third Generation Partnership Project (3GPP) standard, and the major research trends. By providing fundamental notions on wireless localization, comprehensive definitions of measurements and architectures, examples of algorithms, and details on simulation approaches, this paper is intended to represent an exhaustive guide for researchers and practitioners. 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 analyze the performance of 3GPP Rel-16 positioning by standard-compliant simulations in realistic outdoor and indoor propagation environments, investigating the impact of the system configuration and the limitations to be resolved for delivering accurate positioning solutions.