A trie  is an ordered tree data structure that stores keys 
usually represented by strings.  Tries were introduced by 
de la Briandais in 1959 and quickly became one of the most popular data 
structures on words. They are pertinent to (internal) structure of stored 
words and several splitting procedures used in diverse contexts. 
In the first part of this talk we present precise analysis of the profile of
a trie which is defined as the number of nodes (either internal or external) 
with the same distance to the root. It is a function of the number of
strings stored in a trie and the distance from the root.
It appears that the profile of tries exhibits several fascinating
phenomena. When moving from the root to the leaves of a trie, the
growth of the expected profile varies. Near the root, the external
profile is exponentially small (with the number of strings stored),
then it decays in a logarithmic rate until it abruptly
starts growing, first logarithmically and then polynomially; finally, it
tends polynomially to zero again. Furthermore, the expected profile of
asymmetric tries is oscillating in a range where the profile grow
polynomially in contrast to most shape parameters of random tries studied 
previously.  In the second part of the talk we discuss two applications.
One dealing with analysis of an error resilient Lempel-Ziv'77 scheme, and the
other is related to distributed hash tables.