When discussing the topic of elementary complex variables, students are often mystified by the fact that ii is real. After seeing a proof of this statement, a standard question is "well, what about iii or iiii etc., are these real or complex?" In this paper the meaning of the infinite power-tower iii...is considered both from the "bottom-up" and the "top-down." Some surprising graphical representations are revealed and issues of convergence and evaluation are discussed. Finally, we introduce the elementary properties of the Lambert's W-function and it's relationship to the function f(x) = xxxx...which Euler explored in 1783.