Worms are a common phenomenon in today's Internet and cause tens of billions of dollars in damages to businesses around the world each year. This article first presents various concepts related to worms, and then classifies the existing worms into four types- Internet worms, P2P worms, email worms and IM (Instant Messaging) worms, based on the space in which a worm finds a victim target. The Internet worm is the focus of this article. We identify the characteristics of Internet worms in terms of their target finding strategy, propagation method and anti-detection capability. Then, we explore state-of-the-art worm detection and worm containment schemes. This article also briefly presents the characteristics, defense methods and related research work of P2P worms, email worms and IM worms. Nowadays, defense against worms remains largely an open problem. In the end of this article, we outline some future directions on the worm research.