Biomaterials are widely used in diverse applications as substances, materials or important elements of biomedical devices. Biodegradable polymers, both natural and synthetic, have been utilized in applications in which they act as temporary substitutes. Poly(a-hydroxy acids), especially lactic acids and glycolic acid and their copolymers with epsilon-caprolactone, are the most widely known and used among all biodegradable polymers. They degrade in vivo into safe end products mainly by hydrolysis in a few weeks to several months, depending on several factors, including molecular structure/morphology, average molecular weight, size and shape. They are processed into tailor-made materials for diverse applications, although mainly for soft and hard tissue repair. Electrospinning is a method of producing nanofibers and nonwoven matrices from their solutions and melts. Several factors affect fiber diameter and resulting nonwoven structures/morphologies. Recently, electrospun matrices made of lactic acids, glycolic acid and epsilon-caprolactone homo- and co-polymers have been attracting increasing attention for fabrication of novel materials for medical use. This review briefly describes poly(alpha-hydroxy acids) and the elecrospinning process, and gives some selected recent applications of electrospun matrices made from these polymers.