Rule extraction (RE) from recurrent neural networks (RNNs) refers to finding models of the underlying RNN, typically in the form of finite state machines, that mimic the network to a satisfactory degree while having the advantage of being more transparent. RE from RNNs can be argued to allow a deeper and more profound form of analysis of RNNs than other, more or less ad hoc methods. RE may give us understanding of RNNs in the intermediate levels between quite abstract theoretical knowledge of RNNs as a class of computing devices and quantitative performance evaluations of RNN instantiations. The development of techniques for extraction of rules from RNNs has been an active field since the early 1990s. This article reviews the progress of this development and analyzes it in detail. In order to structure the survey and evaluate the techniques, a taxonomy specifically designed for this purpose has been developed. Moreover, important open research issues are identified that, if addressed properly, possibly can give the field a significant push forward.