  We propose to visualize complex (meromorphic) functions $f$ by their phase
$P_f:=f/|f|$. Color--coding the points on the unit circle converts the function
$P_f$ to an image (the phase plot of $f$), which represents the function
directly on its domain. We discuss how special properties of $f$ are reflected
by their phase plots and indicate several applications. In particular we
reformulate a universality theorem for Riemann's Zeta function in the language
of phase plots.
