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 studies into seven broad classes according to their modeling approaches.The classes include: 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 modem 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 Gaia DR2 data are approaching a higher precision.We end with a detailed discussion of future developments in the field,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.