Observed for the first time in 1967 as pulsars, neutron stars
represent the most extreme bodies known in nowadays universe. Relict of the
gravitational collapse and subsequent supernova explosion of a massive
star at the end of its life, they gather a mass of up to twice that of
our sun in a sphere with a radius of about 10 km. Their phenomenology
is very rich and complex. They are not only very compact, but they are
also rotating at frequencies of up to 700 Hz and can have strong
magnetic fields of the order $10^{15}$ G. Their modelling requires many
different fields of physics such as general relativity, nuclear
physics and solid state physics. During this talk, after an
introduction, I will discuss some examples of how the confrontation of
observational data with neutron star models allows one to probe properties
of ultra-dense matter. In the last part of my talk I will present
future prospects on how to obtain additional reliable constraints, among
others from the observations of binary neutron star mergers with
gravitational waves.