The need for reliably determining the identity of a person is critical in a number of different domains ranging from personal smartphones to border security; from autonomous vehicles to e-voting; from tracking child vaccinations to preventing human trafficking; from crime scene investigation to personalization of customer service. Biometrics, which entails the use of biological attributes such as face, fingerprints and voice for recognizing a person, is being increasingly used in several such applications. While biometric technology has made rapid strides over the past decade, there are several fundamental issues that are yet to be satisfactorily resolved. In this article, we will discuss some of these issues and enumerate some of the exciting challenges in this field.