Magnetic levitation systems using HTS bulks, such as magnetic bearing devices for flywheel energy storage systems, transporters, linear actuators, magnetic gears and so on, have been developed by many research groups. Most of the HTS magnetic levitation systems are composed of HTS bulks and permanent magnets. "Stable magnetic levitation without any other control system" is a specific characteristic of the HTS bulks. A non-contact spin processor and a magnetic-levitation seismic isolation device are introduced as magnetic levitation systems that are composed of HTS bulks and permanent magnets. Furthermore, an active magnetic levitation system using spherical HTS bulks for inertial nuclear fusion and a three-dimensional HTS actuator are introduced as magnetic levitation systems with HTS bulks and electromagnets. Levitation force, levitation gap and stability are closely related to the size and shape of the HTS bulk, the magnetic field distribution around the HTS bulk, the conditions in the field-cooling process of the HTS bulk and so on. Achieving large levitation force, large levitation gap and highly stable levitation is very important for practical use of the HTS magnetic levitation system. Theoretical analysis using a numerical simulation code for understanding electromagnetic behaviors within the HTS bulk is useful for improving the levitation force, levitation gap and stability. Finally, numerical techniques based on the finite element method are introduced in this paper.