Investigating anonymity degree offered by communication protocols is 
one of the most challenging problems in computer security. 
This requires providing adequate models capturing essential properties of the real 
protocol execution, finding appropriate quantitative measures, and designing analytic techniques for determining anonymity level expressed with these measures. 

We overview recent advances in this area: information theoretic approach due to Berman, Fiat and Ta-Shma, as well as Markov chain approach and results by Gogolewski, Luczak and ourselves.