  To most mathematicians and computer scientists the word ``tree'' conjures up,
in addition to the usual image, the image of a connected graph with no
circuits. In the last few years various types of trees have been the subject of
much investigation, but this activity has not been exposed much to the wider
mathematical community. This article attempts to fill this gap and explain
various aspects of the recent work on generalized trees.
  The subject is very appealing for it mixes very na\"{\i}ve geometric
considerations with the very sophisticated geometric and algebraic structures.
In fact, part of the drama of the subject is guessing what type of techniques
will be appropriate for a given investigation: Will it be direct and simple
notions related to schematic drawings of trees or will it be notions from the
deepest parts of algebraic group theory, ergodic theory, or commutative algebra
which must be brought to bear? Part of the beauty of the subject is that the
na\"{\i}ve tree considerations have an impact on these more sophisticated
topics and that in addition, trees form a bridge between these disparate
subjects.
