Alginate is an interesting natural biopolymer to be considered for biomedical applications due to its advantages and good biological properties. These biological properties make electrospun alginate nanofibers suitable for various uses in the biomedical field, such as wound healing dressings, drug delivery systems, or both. Unfortunately, the fabrication of alginate nanofibers by electrospinning is very challenging because of the high viscosity of the solution, high surface tension and rigidity in water due to hydrogen bonding, and also their diaxial linkages. This review presents an overview of the factors affecting the electrospinning process of sodium alginate/poly(ethylene oxide) (SA/PEO), the application of SA/PEO in drug delivery systems for wound healing applications, and the degradation and swelling properties of SA/PEO. The challenges and future directions of SA/PEO in the medical field are also discussed.