Robust microfluidic mixing devices mix multiple fluid streams passively, without the use of moving parts. In one embodiment, these devices contain microfluidic channels that are formed in various layers of a three-dimensional structure. Mixing may be accomplished with various manipulations of fluid flow paths and/or contacts between fluid streams. In various embodiments, structures such as channel overlaps, slits, converging/diverging regions, turns, and/or apertures may be designed into a mixing device. Mixing devices may be rapidly constructed and prototyped using a stencil construction method in which channels are cut through the entire thickness of a material layer, although other construction methods including surface micromachining techniques may be used.