Microcalorimeters offer a promising technology for high throughput, high resolution X-ray spectroscopy. A microcalorimeter is, in essence, an ultra sensitive thermometer. It measures the energy of each incident X-ray photon by sensing a tiny increase in temperature of the absorber and then converts the temperature pulse to a measurable electrical pulse, typically by making use of the fact that its electrical resistance of a microcalorimeter is a strong function of temperature. It recovers and is ready for the next X-ray photon, when the heat generated leaks from the absorber to the heat bath of constant temperature; the more quickly the leakage occurs the faster the pulse decays. The accuracy to which a microcalorimeter measures the photon energy is fundamentally limited by thermodynamic fluctuations in the exchange of thermal energy between the absorber and the heat bath, which is proportional to the temperature squared and also to heat capacity. To achieve good spectral resolution, therefore, it is necessary to operate the microcalorimeter at cryogenic temperatures (typically < 100 mK). We are developing X-ray microcalorimeters based on superconducting transition-edge sensor technologies, for a concept mission, known as the Hot Universe Baryon Surveyor (HUBS). The scientific thrust of HUBS is to see the “missing baryons” in circumgalactic and intergalactic media.