Tremendous traffic on the Internet exhibits ON/OFF patterns. In the past, the generation of such ON/OFF traffic was mainly attributed to TCP and application characteristics. Nowadays, however, much traffic is often intentionally shaped into an ON/OFF pattern for achieving certain optimized system performance or resulting from characteristics of some new applications. In this article, we present a comprehensive survey on the ON/OFF traffic shaping in the current Internet. We first introduce the motivations behind ON/OFF traffic shaping in different fields based on different system optimization objectives and application characteristics. We then introduce the impacts of ON/OFF traffic on packet drop probability, real-time applications, and also its interaction with TCP's congestion control mechanism. We further present a survey on existing mechanisms for mitigating these impacts in various aspects. We introduce how each of these mechanisms works, and discuss their merits and deficiencies. Finally, we conclude this article with some future directions for ON/OFF traffic shaping in the Internet.