Weighing the Milky Way and its components has been one of the major goals in Galactic dynamics within the last few decades. Since the total mass of the Galaxy is vastly dominated by the extended dark halo, weighing the entire Galaxy basically boils down to determining the mass profile or gravitational potential of this halo. Various attempts have been made at constraining its virial mass, or the halo mass enclosed within a certain limiting radius, using all kinds of available tracers of the Galactic matter distribution. Some approaches also attempted to constrain the shape of the dark matter distribution, i.e. its flattening or triaxiality. Here we list a few of the more recent measurements, first for the enclosed mass and then for the shape of the dark halo.