  We perform an extensive review of the numerous studies and methods used to
determine the total mass of the Milky Way. We group the various methods into
seven broad classes, including: i) estimating Galactic escape velocity using
high velocity objects; ii) measuring the rotation curve through terminal and
circular velocities; iii) modeling halo stars, globular clusters and satellite
galaxies with the Spherical Jeans equation and iv) with phase-space
distribution functions; v) simulating and modeling the dynamics of stellar
streams and their progenitors; vi) modeling the motion of the Milky Way, M31
and other distant satellites under the framework of Local Group timing
argument; and vii) measurements made by linking the brightest Galactic
satellites to their counterparts in simulations. For each class of methods, we
introduce their theoretical and observational background, the method itself,
the sample of available tracer objects, model assumptions, uncertainties,
limits and the corresponding measurements that have been achieved in the past.
Both the measured total masses within the radial range probed by tracer objects
and the extrapolated virial masses are discussed and quoted. We also discuss
the role of modern numerical simulations in terms of helping to validate model
assumptions, understanding systematic uncertainties and calibrating the
measurements. While measurements in the last two decades show a factor of two
scatters, recent measurements using \textit{Gaia} DR2 data are approaching a
higher precision. We end with a detailed discussion of future developments,
especially as the size and quality of the observational data will increase
tremendously with current and future surveys. In such cases, the systematic
uncertainties will be dominant and thus will necessitate a much more rigorous
testing and characterization of the various mass determination methods.
