Thin liquid films or rivulets may provide very high heat transfer intensity, especially in the micro region near contact-line and may be used for cooling of microelectronic equipment or engines. The paper focuses on the recent progress that has been achieved in the understanding of the rivulet flow phenomena in micro/mini-channels through conducting experiments and theory. Experiments on a gas shear-driven rivulet flow in a minichannel have been done during four parabolic flights campaigns of the European Space Agency. The phase shift schlieren technique and a conventional schlieren technique have been used for two-phase flow visualization. The force balance is varied during a parabolic flight and due to surface tension effect the liquid film in a minichannel 40 mm width became a flattened rivulet 9 mm width at microgravity. The rivulet reaches the certain equilibrium width at microgravity. The numerical calculations of the flow depending on the gravity forces have been made. It was found also that the rivulet width and shape is changing with gravity. The character of shear- and gravity driven rivulet flowing is different at horizontal micro- and minichannels. The comparison of numerical and analytical results with experimental data has been carried out.