The true nature and the internal constitution of the compact stars known as neutron stars (NSs) is one of the most fascinating enigma in modern astrophysics. We discuss some of the present models for the internal structure of NSs and the connection with the properties of ultra dense hadronic matter. In particular, we discuss the role of strangeness on the equation of state and the implications of the measurement of 2 solar mass NSs in PSR J1614-2230 and PSR J0348+0432. Neutron stars (NSs) are

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... comparable natural laboratories that allow us to investigate the fundamental constituents of matter and their interactions under extreme conditions that cannot be reproduced in terrestrial laboratories. The bulk properties and the internal constitution of NSs primarily depend on the equation of state (EoS) of strong interacting matter [1], i.e. on the thermodynamical relation between the matter pressure, energy density and temperature. Determining the correct EoS model describing NS is a fundamental problem of nuclear physics and astrophysics, and a major effort has been made during the last few decades to solve it by measuring different NS properties using the data collected by various generations of X-ray and γ-ray satellites and by ground-based radio telescopes. The rather recent accurate measurement of the masses, M = 1.97 ± 0.04 M sun [2] and M = 2.01 ± 0.04 M sun [3] , of the neutron stars in PSR J1614-2230 and PSR J0348+0432 respectively, has ruled out all the EoS models which cannot support such high values of stellar masses. 201 , 0 0 EPJ Web of Conferences