Electrospinning is a simple, low-cost and versatile approach to fabricate multifunctional materials useful in drug delivery and tissue engineering applications. Despite its emergence into other manufacturing sectors, electrospinning has not yet made a transformative impact in the clinic with a pharmaceutical product for use in humans. Why is this the current state of electrospun materials in biomedicine? Is it because electrospun materials are not yet capable of overcoming the biological safety and efficacy challenges needed in pharmaceutical products? Or, is it that technological advances in the electrospinning process are needed? This review investigates the current state of electrospun materials in medicine to identify both scientific and technological gaps that may limit clinical translation.