Not all radiation is harmful, and whether or not it is harmful depends on the type of radiation in question and how much (the so-called “dose”) you are exposed to.
Some types of radiation are known as “ionising”. Ionising radiation includes both electromagnetic sources, such as X-rays and gamma rays, and particles, such as alpha and beta particles. Naturally-occurring radon gas, for example, emits alpha particles. Ionising radiation can cause burns, radiation sickness, and cancer.
Some types of non-ionising radiation can also be harmful. For example, using a sunbed or staying out in the sun too long will expose you to ultraviolet radiation, which can cause premature ageing, cataracts and skin cancer.
Other types of non-ionising radiation, such as lasers, can cause burns and eye damage.