Nonlinear dynamic and mechanic responses of entangled polymeric liquids to external deformations determine processing behavior of a hundred billion pounds of thermoplastic and rubber materials that are produced every year. The emerging phenomenology and theoretical concepts suggest that we need to go beyond the conventional description of polymer rheology involving high external deformations. The new understanding emphasizes the need to monitor the deformation field without predicating that homogeneous deformation would prevail in these highly viscoelastic materials. Entangled polymeric liquids are transient soft solids with finite cohesion and necessarily have to transform from a solid-like network state to a state of flow. Apparently, this yielding often results in inhomogeneous flow. About two dozen movies of particle-tracking velocimetric observation and publications can be found at our website: http://www3.uakron.edu/rheology/