  Arrays of low-temperature microcalorimeters provide a promising technology
for X-ray astrophysics: the imaging spectrometer. A camera with at least
several thousand pixels, each of which has an energy-resolving power ($E/\Delta
E\urss{FWHM}$) of a few thousand across a broad energy range (200~eV to 10~keV
or higher), would be a revolutionary instrument for the study of energetic
astrophysical objects and phenomena. Signal readout is a critical enabling
technology. Multiplexed readout, in which signals from multiple pixels are
combined into a single amplifier channel, allows a kilo pixel-scale
microcalorimeter array to meet the stringent requirements for power
consumption, mass, volume, and cooling capacity in orbit. This chapter
describes three different multiplexed-readout technologies for
transition-edge-sensor microcalorimeters: time-division multiplexing,
frequency-domain multiplexing, and microwave-SQUID multiplexing. For each
multiplexing technique, we present the basic method, discuss some design
considerations and parameters, and show the state of the art. The chapter
concludes with a brief discussion of future prospects.
