  The so called "hyperon puzzle", i.e. the difficulty to reconcile the measured
masses of neutron stars (NSs) with the presence of hyperons in their interiors,
is one of the hot topics in astrophysics which is stimulating copious
experimental and theoretical research in hypernuclear physics. After
illustrating the origin of the hyperon puzzle, I discuss some of its possible
solutions, and particularly those related to the role of hyperonic two- and
three-body interactions on the equation of state of dense matter. Afterward, I
discuss a possibility to circumvent the hyperon puzzle allowing for the
presence of strangeness in NSs in the form of deconfined strange quark matter,
and thus considering the so called quark stars, i.e. hybrid stars or strange
stars. Finally I discuss the astrophysical consequences of the possible
conversion process of an hadronic star to a quark star.
