This book provides a survey on different kinds of Feistel ciphers, with their definitions and mathematical/computational properties. Feistel ciphers are widely used in cryptography in order to obtain pseudorandom permutations and secret-key block ciphers. In Part 1, we describe Feistel ciphers and their variants. We also give a brief story of these ciphers and basic security results. In Part 2, we describe generic attacks on Feistel ciphers. In Part 3, we give results on DES and specific Feistel ciphers. Part 4 is devoted to improved security results. We also give results on indifferentiability and indistinguishability.