This chapter introduces the reader to a group of papers which deal with the inference of grammar rules using discrete-time recurrent neural networks (DTRNN). Section 5.1 defines the problem of grammatical inference. The use of DTRNN for grammatical inference is discussed in section 5.2. The fact that DTRNN capable of representing some tasks may not be able to learn them is the subject of section 5.3. Section 5.4 discusses the algorithms that may be used to extract finite-state machines from trained DTRNN. Finally, section 5.5 introduces the featured papers by dividing them in two main groups: papers dealing with the inference of finite-state machines and papers dealing with the inference of context-free grammars.