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Surface tension-driven self-alignment is a passive and highly-accurate positioning mechanism that can significantly simplify and enhance the construction of advanced microsystems. After years of research, demonstrations and developments, the surface engineering and manufacturing technology enabling capillary self-alignment has achieved a degree of maturity conducive to a successful transfer to industrial practice. In view of this transition, a broad and accessible review of the physics, material science and applications of capillary self-alignment is presented. Statics and dynamics of the self-aligning action of deformed liquid bridges are explained through simple models and experiments, and all fundamental aspects of surface patterning and conditioning, of choice, deposition and confinement of liquids, and of component feeding and interconnection to substrates are illustrated through relevant applications in micro- and nanotechnology. A final outline addresses remaining challenges and additional extensions envisioned to further spread the use and fully exploit the potential of the technique.