The need for very good energy resolution in experiments in particle and astroparticle physics and the need to detect very small energy depositions are the major motivations for the development of low-temperature particle detectors. Because the energy quanta associated with superconductors and lattice vibrations (phonons) are more than one hundred times smaller, substantial improvements have been obtained in energy resolution and in sensitivity over conventional detectors. Furthermore, these detection schemes permit tailoring of target or absorber materials to match the physics requirements. In this article, the basic physics principles behind various methods of detecting excitations induced by particle interactions in bulk single-crystal materials at low temperatures are reviewed. We also present an overview of progress toward implementation of particle physics experiments, such as detection of low-energy neutrinos, search for dark-matter particles, search for neutrino-less double β decay, and βand γ -ray spectroscopy and X-ray astronomy using low-temperature detectors.