Proxy signature is a specific digital signature, which allows an original signer to delegate her signing capability to proxy signer and then, the later can perform message signing on behalf of the former. Authentication is a desired property in cryptographic protocols. The proxy signature provides this property. In this article, we cover the research progress made on proxy signature and investigate its relationships with other existing signature schemes having continuous progress until now. We also provide real-world scenarios, to understand better the situations, where these schemes are applicable for security purposes. We analyze the security properties of existing schemes and make a comparison among them on the basis of different number theoretic problems. Some open problems are also discussed, to the best of our knowledge. In addition, we provide some future directions, which can be used as a hint to work further in the area of proxy signature. We hope that this article will provide a ready reference to work in the related area. Copyright © 2012 John Wiley & Sons, Ltd.