Dynamical systems play a central role in the design of symmetric cryptosystems. Their use has been widely investigated both in ''chaos-based'' private communications and in stream ciphers over finite fields. In the former case, they get the form of automata named as Moore or Mealy machines. The main charateristic of stream ciphers lies in that they require synchronization of complex sequences generated by the dynamical systems involved at the transmitter and the receiver part. In this paper, we focus on a special class of symmetric ciphers, namely the Self-Synchronizing Stream Ciphers. Indeed, such ciphers have not been seriously explored so far although they get interesting properties of synchronization which could make them very appealing in practice. We review and compare different design approaches which have been proposed in the open literature and fully-specified algorithms are detailed for illustration purpose. Open issues related to the validation and the implementation of Self-Synchronizing Stream Ciphers are developped. We highlight the reason why some concepts borrowed from control theory appear to be useful to this end.