Manipulating particles and cells in magnetic liquids through "negative magnetophoresis" is a new research field. It has resulted in label-free and low-cost manipulation techniques in microfluidic systems and many exciting applications. It is the goal of this review to introduce the fundamental principles of negative magnetophoresis and its recent applications in microfluidic manipulation of particles and cells. The theoretical background of three commonly used specificities of manipulation in magnetic liquids is first discussed, including the size, density and magnetic property of particles and cells. This is followed by a review and comparison of the media used in negative magnetophoresis, which include paramagnetic salt solutions and ferrofluids. Afterwards, the existing microfluidic applications of negative magnetophoresis are reviewed, including separation, focusing, trapping and concentration of particles and cells, determination of cell density, measurement of particles' magnetic susceptibility, and others. The need for developing biocompatible magnetic liquids for live cell manipulation and analysis and its recent progress are also examined. Finally, the review is concluded with a brief outlook for this exciting research field.