A review of cryogenic particle detectors is presented. A major motivation for developing this type of particle detector is their superior sensitivity to weakly ionizing particle interactions. This makes them suitable devices for detecting solar neutrinos via the coherent neutrino scattering off nuclei and for detecting non-baryonic dark matter candidates in our galactic halo. Cryogenic particle detectors have reached, and in some cases already surpassed, the high energy resolution of the best semiconducting detectors, and they have the potential of becoming the next generation of high-resolution detectors. The emphasis of this review is on the basic condensed matter physics of these low-temperature detectors and to present an overview of the present experimental status.