The preparation of core-sheath fibers by electrospinning is a topic of significant interest for producing composite fibers with distinct core and sheath functionalities. Moreover, in core-sheath fibers, low-molecular-weight substances or nanosized inorganic additives can be deposited in a targeted manner within the core or the sheath. Commonly, for obtaining a core-sheath structure, coaxial electrospinning is used. It requires a coaxial spinneret and suitable immiscible solvents for the inner and outer solutions. The single-nozzle spinneret electrospinning of emulsions can address these issues, but use of a stabilizing agent is needed. A third approach-preparation of core-sheath fibers by single-nozzle spinneret electrospinning of homogeneous blend solutions of two polymers or of a polymer/low-molecular-weight substance-has been much less studied. It circumvents the difficulties associated with the coaxial and the emulsion electrospinning and is thoroughly discussed in this review. The formation of core-sheath fibers in this case is attributed to phase-separation-driven self-organization during the electrospinning process. Some possibilities for obtaining core-double sheath fibers using the same method are also indicated. The gained knowledge on potential applications of core-sheath fibers prepared by single-nozzle spinneret electrospinning of emulsions and homogeneous blend solutions is also discussed.