First observed in 1995, the top quark is one of a pair of third-generation quarks in the Standard Model of particle physics. It has charge +2/3e and a mass of 171.4 GeV, about 40 times heavier than its partner, the bottom quark. The CDF and D0 collaborations have identified several hundred events containing the decays of top-antitop pairs in the large dataset collected at the Tevatron proton-antiproton collider over the last four years. They have used these events to measure the top quarks mass to nearly 1% precision and to study other top quark properties. The mass of the top quark is a fundamental parameter of the Standard Model, and knowledge of its value with small uncertainty allows us to predict properties of the as-yet-unobserved Higgs boson. This paper presents the status of the measurements of the top quark mass.