A weak asthenosphere, or low‐viscosity zone (LVZ), underlying Earth's lithosphere has played an important role in interpreting isostasy, postglacial rebound (PGR), and the seismic LVZ, as well as proposed mechanisms for continental drift, plate tectonics, and postseismic relaxation. Consideration of the resolving power of PGR, postseismic relaxation, and geoid modeling studies suggests a sublithospheric LVZ perhaps ~100–200 km thick with a viscosity contrast of ~100–1,000. Ab initio numerical models of plate‐like boundary layer motions in mantle convection also suggest a key role for the LVZ. Paradoxically, a thinner LVZ with a strong viscosity contrast is most effective in promoting plate‐like surface motions. These numerical results are explained in terms of the reduction in horizontal shear dissipation due to an LVZ, and a simple scaling theory leads to somewhat nonintuitive model predictions. For example, an LVZ causes stress magnification at the base of the lithosphere, enhancing plate boundary formation. Also, flow within the LVZ may be driven by the plates (Couette flow), or pressure‐driven from within the mantle (Poiseuille flow), depending upon the degree to which plates locally inhibit or drive underlying mantle convection. For studies of the long‐wavelength geoid, PGR, and mantle convection, a simple dimensionless parameter controls the effect of the LVZ. This “Cathles parameter” is given by Ct = η*(D/λ)3, where η* is the viscosity contrast, D is the thickness of the LVZ, and λ is the flow wavelength, emphasizing the tightly coupled trade‐off between LVZ thickness and viscosity contrast.