Pressure, together with temperature and magnetic field, is an important thermodynamical parameter in physics. Investigating the response of a compound or of a material to pressure allows to elucidate ground states, investigate their interplay and interactions and determine microscopic parameters. Pressure tuning is used to establish phase diagrams, study phase transitions and identify critical points. Muon spin rotation/relaxation (μSR) is now a standard technique making increasing significant contribution in condensed matter physics, material science research and other fields. In this review, we will discuss specific requirements and challenges to perform μSR experiments under pressure, introduce the high pressure muon facility at the Paul Scherrer Institute (PSI, Switzerland) and present selected results obtained by combining the sensitivity of the μSR technique with pressure.