Heave compensator is a system that mitigates transmission of heave movement from vessels to the equipment in the vessel. In drilling industry, a heave compensator enables drilling in offshore environments. Heave compensator attenuates movement transmitted from the vessel to the drill string and drill bit ensuring security and efficiency of the offshore drilling process. Common types of heave compensators are passive, active and semi-active compensators. This article presents 4 main points. First, a bulk modulus analysis obtains a simple condition to determine if the bulk modulus can be neglected in the design of hydropneumatic passive heave compensator. Second, the methodology to design passive heave compensators with the desired frequency response. Third, four control methodologies for semi-active heave compensator are tested and compared numerically. Lastly, we show experimental results obtained from a prototype with the methodology developed to design passive heave compensator.