Suppose one has a polynomial equation in two variables, $f(x,y)=0$. This defines a curve, but if we work over the complex numbers, it in fact defines a surface in $C^2$, which is difficult to visualize. I will discuss ways of visualizing these surfaces by introducing the concepts of amoebas, and their relationship to a new notion known as tropical geometry. \vskip .2in \noindent Refreshments will be served!