3D human motion generation and simulation is an important area of research with applications in virtual reality, gaming, animation, robotics, and AI-driven content creation. Generating realistic and controllable human motion is essential for creating interactive digital environments, improving character animation, and enhancing human-computer interaction. Recent advances in deep learning have made it possible to automate motion generation, reducing the need for expensive motion capture and manual animation. Techniques such as diffusion models, generative masking, and variational autoencoders (VAEs) have been used to synthesize diverse and realistic human motion. Transformer-based models have improved the ability to capture temporal dependencies, leading to smoother and more natural movement. In addition, reinforcement learning and physics-based methods have helped create physically consistent and responsive motion, which is useful for applications like robotics and virtual avatars. This tutorial will bridge the gap between computer vision, graphics, and robotics, providing a comprehensive guide to the latest methods, practical applications, and future challenges. This tutorial will be organized into six core parts, guiding you from foundational knowledge to advanced research frontiers: (1) Human Motion Generation Basics: introducing fundamentals, key concepts and data representations; (2) Kinematic-Based Generation Methods: explore popular data-driven techniques that learn from motion capture datasets to produce lifelike animations; (3) Physics-Based Generation Methods: dive into methods that use reinforcement learning and physics simulations to create physically consistent and responsive motion; (4) Controllability of Human Motion Generation: learn how to direct and control motion synthesis using inputs like text, audio, or specific goals; (5) Human-Object/Human/Scene Interactions: cover advanced scenarios involving complex interactions with objects, other people, and the surrounding environment, and (6) Open Research Problems: discussing the major unsolved challenges and exciting opportunities for future work in the field.