We present in this article an overview of the problem of neutron star masses. After a brief appraisal of the methods employed to determine the masses of neutron stars in binary systems, the existing sample of measured masses is presented, with a highlight on some very well-determined cases. We discuss the analysis made to uncover the underlying distribution and a few robust results that stand out from them. The issues related to some particular groups of neutron stars originated from different channels of stellar evolution are shown. Our conclusions are that last centurys paradigm that there a single, $1.4 M_{odot}$ scale is too simple. A bimodal or even more complex distribution is actually present. It is confirmed that some neutron stars have masses of $sim 2 M_{odot}$, and, while there is still no firm conclusion on the maximum and minimum values produced in nature, the field has entered a mature stage in which all these and related questions can soon be given an answer.
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