The hydrodynamic characteristics of hybrid fluid made of liquid metal/aqueous solution are elementary in the design and operation of conductive flow in a variety of newly emerging areas such as chip cooling, soft robot, and biomedical practices. In terms of physical and chemical properties, such as density, thermal conductivity and electrical conductivity, their huge differences between the two fluidic phases remain a big challenge for analyzing the hybrid flow behaviors. Besides, the liquid metal immersed in the solution can move and deform when administrated with non-contact electromagnetic force, or even induced by redox reaction, which is entirely different from the cases of conventional contact force. Owing to its remarkable capability in flow and deformation, liquid metal immersed in the solution is apt to deform on an extremely large scale, resulting in marked changes on its boundary and interface. However, the working mecha- nisms of the movement and deformation of liquid metal lack appropriate models to describe such scientific issues via a set of well-established unified equations. To promote investigations in this important area, the present paper is dedicated to summarizing this unconventional hydrodynamics from experiment, theory, and simulation. Typical experimental phenomena and basic working mechanisms are illustrated, followed by the movement and deformation theories to explain these phenomena. Several representative simulation methods are then proposed to tackle the governing functions of the electrohydrodynamics. Finally, prospects and challenges are raised, offering an insight into the new physics of the hybrid fluid under applied fields.