With the recent developments in microfluidic instruments and devices, various types of micrometer-sized materials have been produced by employing multiphase flow patterns formed in the microchannel. In particular, microparticles and microfibers, which are compatible with biomolecule incorporation or living cell encapsulations, have been gaining significant attention as new tools for biochemical analysis, cellular physiological studies, tissue engineering, cell transplantation, and controlled drug delivery. Herein, we introduce recent developments in microfluidic systems to produce alginate-based hydrogel microparticles and microfibers. By utilizing droplet dispersions either in equilibrium or non-equilibrium states, or by employing parallel laminar flows, microengineered functional materials that are difficult to generate using conventional devices and operations can be obtained. New and interesting multiphase phenomena are reviewed, together with the pros and cons of these systems and their applications. Furthermore, the fundamentals of multiphase microfluidics and the materials used to prepare particles and fibers are briefly introduced.