I will review some of the basic ideas and applications of mixes, the standard building block of anonymous communication introduced by Chaum. After that I will describe a new cryptographic technique that we called _universal re-encryption_. A conventional cryptosystem that permits re-encryption, such as ElGamal, does so only for a player with knowledge of the public key corresponding to a given ciphertext. In contrast, universal re-encryption can be done without knowledge of public keys. I will describe an asymmetric cryptosystem with universal re-encryption that is half as efficient as standard ElGamal in terms of computation and storage. While technically and conceptually simple, universal re-encryption leads to new types of functionality in mixnet architectures. Conventional mixnets are often called upon to enable players to communicate with one another through channels that are externally anonymous, i.e., that hide information permitting traffic-analysis. Universal re-encryption lets us construct a mixnet of this kind in which servers hold no public or private keying material, and may therefore dispense with the cumbersome requirements of key generation, key distribution, and private-key management. I will describe two practical mixnet constructions, one involving asymmetric input ciphertexts, and another with hybrid-ciphertext inputs. I will also describe application to privacy for RFID tags. This is joint work with Philippe Golle, Markus Jakobsson, and Ari Juels. The paper is forthcoming at CT-RSA and is available on my web site