The `Extended Projection Principle` (EPP) has been a pervasive topic of research and a pervasive mystery since it was first formulated by Chomsky (1981). That initial formulation is not precise, but its intention is clear enough: The EPP (here called by Chomsky `principle P`) "is the structural requirement that certain configurations … must have subjects …" [p.27] Over the years since, its existence as an independent constraint has often been called into question, on the grounds that it is redundant with other principles, especially those concerning Case (by Fukui and Speas (1986) for example), or that it is literally unformulable given other theoretical desiderata (Epstein and Seely (1999)). I will review those arguments. I will also survey a range of phenomena involving infinitival constructions that provide strong empriical evidence for the EPP. In particular, I will show that in ECM constructions, while the ECM subject sometimes raises overtly to a canonical Case positon (Spec of AgrO), it also sometimes remains in embedded subject position, a position that it is in solely to satisfy the EPP (Lasnik (2001b)). The next question is just how the EPP is to be formulated. Alexiadou and Anagnostopoulou (1998) argue that there are actually two different kinds of languages with respect to the EPP, those (like Greek) where X˚movement suffices versus those where only an XP can satisfy the EPP. I will examine English, a matter of strong feature checking, as in Chomsky (1995), or the requirement that certain functional heads require a specifier, as in Chomsky`s original version and the more recent one in Chomsky (2000). This question turns out to be surprisingly intricate, with arguments for the strong feature version (Merchant 92001), and against it (Lasnik (2001a)).