  The top quark is the heaviest elementary particle known and its mass ($m_{\rm
top}$) is a fundamental parameter of the Standard Model (SM). The $m_{\rm top}$
value affects theory predictions of particle production cross-sections required
for exploring Higgs-boson properties and searching for New Physics (NP). Its
precise determination is essential for testing the overall consistency of the
SM, to constrain NP models, through precision electroweak fits, and has an
extraordinary impact on the Higgs sector, and on the SM extrapolation to
high-energies. The methodologies, the results, and the main theoretical and
experimental challenges related to the $m_{\rm top}$ measurements and
combinations at the Large Hadron Collider (LHC) and at the Tevatron are
reviewed and discussed. Finally, the prospects for the improvement of the
$m_{\rm top}$ precision during the upcoming LHC runs are briefly outlined.
