SQUID multiplexers make it possible to build arrays of thousands of low-temperature bolometers and microcalorimeters based on superconducting transition-edge sensors with a manageable number of readout channels. We discuss the technical tradeoffs between proposed time-division multiplexer and frequency-division multiplexer schemes and motivate our choice of time division. Our first-generation SQUID multiplexer is now in use in an astronomical instrument. We describe our second-generation SQUID multiplexer, which is based on a new architecture that significantly reduces the dissipation of power at the first stage, allowing thousands of SQUIDs to be operated at the base temperature of a cryostat.