  Pressure, together with temperature, electric and magnetic fields, alters the
system and allows to investigate the fundamental properties of the matter.
Under applied pressure the interatomic distances shrink, which modify
interactions between atoms and may lead to appearance of a new (sometime
exotic) physical properties as, e.g., pressure induced phase transition(s);
quantum critical points(s), new structural, magnetic and/or superconducting
states; changes of the temperature evolution and the symmetry of the order
parameter(s) etc. The muon-spin rotation/relaxation ($\mu$SR) appears to be a
commonly used powerful technique allowing to study the magnetic and
superconducting responses of various materials under extreme conditions. At
present, $\mu$SR experiments might be performed under the high magnetic field
up to $\simeq 9$ T, temperatures down to $\simeq 10-15$ mK and hydrostatic
pressure up to $\simeq 2.8$ GPa. In the following Perspective paper the
requirements to the $\mu$SR under pressure experiments, the existing
high-pressure muon facility at the Paul Scherrer Institute (Switzerland), and
selected experimental results obtained by using the $\mu$SR under pressure
technique are discussed.
