Abstract: Aiming at the long unsolved issue of vortex definition, this article reviewed critically those historically appeared definitions, and thereby proposes that the general goal of vortex definition should reflect an inherent combination of the solenoidal nature of vortices in kinematics and their role as the sinews and muscles of fluid motion in dynamics. The definition should, in a unified manner, cover all mature achievements of classic vortex dynamics and guide the identification of complex vortical structures and interactions in turbulence. Thus, on the basis of the known evolution laws of vorticity field, we propose a dynamic definition of vortices as a reference of further discussion. Although various "vortex criteria" constructed for visualizing turbulent structures have played important role in one's understanding, they cannot replace a complete vortex definition since they do not follow the causal evolution rules of the solenoidal vorticity field. In contrast, it is expected that the vorticity-surface theory formed in the past decade will, in its future development, be able to bring the definition of vortex and its testing back to the natural laws of vorticity dynamics.