Particle and radiation detectors have a large number of applications in many different fields like high energy physics, astro-particle physics, nuclear physics, medicine, biology, and even in art and other fields. The article describes the basic interaction processes for typical detectors and their applications used in many different fields. Special emphasis is put on detectors for high resolution spectroscopy. In this respect the best results are obtained with cryogenic detectors which benefit from the low energy required to achieve quantum transitions, in contrast e.g. to ionisation processes. These detection techniques are particularly important for the measurement of low energy particles and rare proceses, like the search for weakly interacting massive particles, which are used in this article as an example for the research possibilities for cryogenic detectors.