During the last years it became quite popular to visualize complex (analytic)
functions as images. The talk gives an introduction to ``phase plots''
(or ``phase portraits''), which depict a function $f$ directly on its domain
by color-coding the argument of $f$. Phase portraits are like fingerprints: though part of the information (the modulus) is neglected, meromorphic functions are (almost) uniquely
determined by their phase plot -- and the first part of the lecture will explain how properties of a function can be recovered.

In the second part we investigate the phase plots of
special functions and illustrate several known results (theorems of
Jentzsch and Szegö, universality of the Riemann zeta function).

Finally we give a few examples which demonstrate that phase plots
and related ``phase diagrams'' are useful tools for exploring complex
functions in teaching and research.