Poly(lactic acid) (PLA) is a synthetic polyester that has shown extensive utility in tissue engineering. Synthesized either by ring opening polymerization or polycondensation, PLA hydrolytically degrades into lactic acid, a metabolic byproduct, making it suitable for medical applications. Specifically, PLA nanofibers have widened the possible uses of PLA scaffolds for regenerative medicine and drug delivery applications. The use of nanofibrous scaffolds imparts a host of desirable properties, including high surface area, biomimicry of native extracellular matrix architecture, and tuning of mechanical properties, all of which are important facets of designing scaffolds for a particular organ system. Additionally, nanofibrous PLA scaffolds hold great promise as drug delivery carriers, where fabrication parameters and drug-PLA compatibility greatly affect the drug release kinetics. In this review, we present the latest advances in the use of PLA nanofibrous scaffolds for musculoskeletal, nervous, cardiovascular, and cutaneous tissue engineering and offer perspectives on their future use.