HOVER is a multi-functional neural full-body controller designed for humanoid robots. It provides universal motion skills by imitating full-body movements and learns various full-body control modes. HOVER integrates different control modes into a unified strategy through a multi-modal policy distillation framework, enabling seamless transitions between different control modes while retaining each mode's unique advantages. This controller enhances the control efficiency and flexibility of humanoid robots across multiple modes, offering a robust and scalable solution for future robotic applications.