This paper deals with the problem of synchronization of chaotic systems when the driven (slave, receiver) system has the same structure as the master (driving, emitter) system but its parameters are unknown. It is shown that the concept of synchronization provides an efficient way to find the unknown slave system parameters. Parameter mismatch between master and slave systems and high sensitivity of response to changes of these parameters were so far considered as crucial for security issues. This paper shows evidence that this claimed advantage becomes in fact a major drawback in chaos communication schemes since parameters ran easily be found using adaptive synchronization and optimization tools. The general problem of identifiability of chaotic systems is defined and discussed in the context of possibilities for finding the unknown chaotic receiver parameters. Several typical systems used in experiments in chaos communication are tested for identifiability showing direct applications of the introduced concepts. In particular examples of the skew tent map, Henon map, Markov maps and Chua's circuit are considered in detail illustrating the problems of global and local identifiability.