  We address the role of multiplicative stochastic processes in modeling the
occurrence of power-law city size distributions. As an explanation of the
result of Zipf's rank analysis, Simon's model is presented in a mathematically
elementary way, with a thorough discussion of the involved hypotheses. Emphasis
is put on the flexibility of the model, as to its possible extensions and the
relaxation of some strong assumptions. We point out some open problems
regarding the prediction of the detailed shape of Zipf's rank plots, which may
be tackled by means of such extensions.
