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The application scenarios and requirements are more diverse in the fifth-generation (5G) era than before. In order to successfully support the system design and deployment, accurate channel modeling is important. Ray-tracing (RT) based deterministic modeling approach is accurate with detailed angular information and is a suitable candidate for predicting time-varying channel and multiple-input multiple-output (MIMO) channel for various frequency bands. However, the computational complexity and the utility of RT are the main concerns of users. Aiming at 5G and beyond wireless communications, this paper presents a comprehensive tutorial on the design of RT and the applications. The role of RT and the state-of-the-art RT techniques are reviewed. The features of academic and commercial RT based simulators are summarized and compared. The requirements, challenges, and developing trends of RT to enable the visions are discussed. The practices of the design of high-performance RT simulation platform for 5G and beyond communications are introduced, with the publicly available high-performance cloud-based RT simulation platform as the main reference. The hardware structure, networking, workflow, data flow and fundamental functions of a flexible high-performance RT platform are discussed. The applications of high-performance RT are presented based on two 5G scenarios, i.e., a 3.5 GHz Beijing vehicle-to-infrastructure scenario and a 28 GHz Manhattan outdoor scenario. The questions on how to calibrate and validate RT based on measurements, how to apply RT for mobile communications in moving scenarios, and how to evaluate MIMO beamforming technologies are answered. This tutorial will be especially useful for researchers who work on RT algorithms development and channel modeling to meet the evaluation requirements of 5G and beyond technologies.