There has been a steady progress in developing synthetic fibers in the past few years. Bicomponent fibers and nanofibers in a core/shell (C/S) configuration, including two dissimilar materials have presented unusual potential for use in many novel applications. These fibers can be produced using a variety of materials via different techniques i.e., coaxial melt spinning and electrospinning. In this review, we discuss the recent advances in C/S fibers and nanofibers' production. The first part has been assigned to the bicomponent fibers manufacturing technology, while production and applications of C/S nanofibers have been described in the second part. (c) 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018, 135, 46265.