Because ionizing radiation does just that, ionizes, it is easy to see that using a medium like a gas, and a voltage, you can measure the amount of charge liberated in that medium. And that is the most common method of measuring radiation. The infamous Geiger Counter is in reality a small volume of gas, with a voltage applied across it. As the radiation enters the gas, it causes electrons to be formed which are collected and measured to determine the amount of initial radiation present. While a little more complicated than that, the processes used with radiation detection is called scintillation.
Scintillation is the giving off of visible light after interaction with radiation.
The light can be collected and used as another measure of the radiation intensity and energy. But, there are many different ways of measuring radiation, using semiconductors, liquids, superheated bubbles, crystals and plastics. The applications of radiation are numerous. For the most part, what radiation does is create ions in our cells, and these ions cause problems in the cell. The radiation may interact directly with biologically significant molecules, like DNA and proteins.