The development of simple and generic principles for microfluidics should have an impact on a wide range of distinct areas, [1] including chemical synthesis, [2] medical diagnostics, [3] and designer emulsions. [4] For advanced applications such as the purification of nucleic acids from a large number of cells, [5] multiple connection of liquid-core/liquid-cladding waveguides, [6] and sorting colloidal emulsions or vesicles in complex solutions, [7][8][9] a high level of selectivity in a highly branched architecture is an essential element of designing a robust platform. However, existing technologies including an electro-kinetic [10] or a hydrodynamic [11] method, successfully employed for a simple or parallel Y-channel structure with a single junction, are not easily applicable for serial branches, due to the requirement of either a high voltage (or pressure) between the junctions or a complicated structure.Herein, we present a concept of nematofluidics that provides a simple, programmable, and hierarchically branched architecture of microfluidics where a nematic liquid crystal (LC) is used as an anisotropic fluid. This anisotropic-fluid-based approach allows precise and concurrent control of the flow resistance and streamlines in multi-junction networks, in analogy to the resistance and current in electrical circuits, by the application of a low electric field to each channel. The anisotropic flow resistance, associated with the nematodynamic viscosities, [12] is electrically controlled through molecular reorientation to steer nano-or microparticles immersed in the LC into a specific channel at each junction. Moreover, due to the channel-independent controllability of the LC, a hierarchically branched architecture of microfluidics with high-level of selectivity is designed.For the flow selection capability at a channel junction, two different microfluidic environments that can be switched are required, namely the effective dynamic viscosity along the flow direction (h 1 ) and that perpendicular to the flow direction (h 3 ). The perpendicular viscosity h 3 is much larger than the parallel shear viscosity h 1 because the rotational motion of the LC molecules is mostly involved in the former. The backflow effect incurred during the switching of one environment to the other should not play a significant role in the steady state.[12] Note that dynamic viscosities will depend on the surface interactions of the LC with a wall as well as the geometric shape of a channel, particularly in a microfluidic system with a high surface-tovolume ratio.In our case, the anisotropic nature of the nematodynamic viscosities is produced through the change in the direction of the LC alignment by an electric field applied perpendicular to the flow. A LC material, 4-cyano-4'-pentylbiphenyl (5CB), was filled into a rectangular microfluidic channel with a cross section of 100 mm in width (w) and 15 mm in height (h), by capillary action. The contact angles of the LC on the glass substrate and on polydimethylsiloxane (PDMS) were measured a...