  For many purposes it is desirable to have an easily understandable and
accurate picture of the atomic states. This is especially true for the highly
excited states which exhibit features not present in the well known states
hydrogen-like orbitals with usual values of the quantum numbers. It could be
expected that such visualizations are readily available. Unfortunately, that is
not the case. We illustrate the problems by showing several less fortunate
earlier presentations in some scientifically most valuable works, and show more
suitable visualizations for those cases. The selected cases are not chosen to
criticize the authors' approach. Rather, we have taken these very important
papers to underline the need for serious work with graphical representations
which this work attempts to be a part of.
  In this text we discuss the problems encountered when visualizing Rydberg
states, review some existing presentations and propose guidelines for
applications. The focus of this work are so called Stark states and coherent
elliptic states of Rydberg atoms. In the sections on elliptic states we show
some quite novel geometric interpretations which should be very helpful in
analysis of Rydberg state manipulations in external fields.
  Our demonstration examples involve only hydrogen-like states. However, the
techniques and analysis are also relevant for Rydberg molecules and more
complicated highly excited atomic and molecular systems.
