This master thesis presents the development, analysis and comparison of different heave compensator methodologies for drill string.Firstly, a review of previous studies about the subject is presented. Next, is presented a study of drill string modelling. Following the studies, a methodology to design a passive heave compensator is develop and validated by using a small scale prototype. In order to obtain higher levels of attenuation, active heave compensators are designed.Hence, the study of observers, estimators and filters, such as Kalman filter is developed. Three methodologies of active controls are presented, pole placement, pole placement with disturbance rejection using flatness and backstepping robust control. Finally, numerical simulations results are presented and analysed.