The term ‘pied-piping’ is used by linguists to refer to structures where a movement operation applies to a constituent that is in some sense ‘larger than expected’. More precisely, pied-piping occurs when a movement operation that usually targets expressions of a particular type (e.g. wh-words) instead targets a phrase that contains an expression of that type. Pied-piping structures have long been a deep and difficult puzzle for formal syntactic theory. This is the first of two articles that present and compare two recent approaches to pied-piping, those of Cable (2010a,b) and Heck (2008, 2009). These works offer two very different perspectives on the nature of pied-piping, and thus yield rather different analyses of specific sub-phenomena. Nevertheless, there is much overlap in their general predictions and in several core assumptions. In this article, I present the basic phenomenon of pied-piping, as well as general summaries of Cable (2010a,b) and Heck (2008, 2009). I also explain why these works eschew the mechanism of ‘feature percolation’, an operation which has until recently been a staple of much work on pied-piping.