The so called hyperon puzzle in neutron stars, i.e. the difficulty to reconcile the measured masses of neutron stars 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 and dense matter physics. After illustrating the origin of the hyperon puzzle, I will 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 will discuss a possibility to circumvent the hyperon puzzle allowing for the presence of strangeness in neutron stars 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 will discuss the astrophysical consequences of the possible conversion process of an hadronic star to a quark star.