The development of cryogenic detectors is largely motivated by the need for very good energy resolution in a number of particle physics experiments, and by the need to detect very small energy depositions. Good energy resolution can be obtained by utilizing the smallness of the superconducting energy gap or detecting the phonons which are produced by particle interactions. These detection schemes require low temperatures, where in addition the thermal fluctuations are small compared to the minute energies expected to be deposited in some experiments. Moreover, cryogenic detectors permit the tailoring of the target or absorber materials to match the particle physics goals. The basic physics behind the detection of excitations induced by particle interactions in bulk single crystal materials is reviewed, and recent results on the efficient detection of these excitations with series arrays of superconducting tunnel junctions are presented. Progress towards the implementation of particle physics experiments, such as the detection of low energy solar neutrinos, search for dark matter particles, search for neutrinoless double beta-decay and precision observation of a 17 keV neutrino in beta-decay, using cryogenic detectors is reviewed.