You may be asked to have investigations done in the radiology department.  There are different types of tests that may be performed.

Plain x-ray: eg. chest x-ray or abdominal x-ray or mammograms. These are done very frequently. All x-rays involve a small amount of exposure to radiation. Radiation in high doses can sometimes cause cancer. Plain x-rays are associated with very low risk.

Ultrasound: eg ultrasound of gallbladder.  Ultrasound does not involve radiation and is very safe. However it is only suitable for certain organs.

CT ("CAT") scan: CT stands for computed tomography. These scans involve the most radiation exposure. It is performed judiciously and only if necessary. These scans are avoided in pregnancy.

MRI: MRI stands for magnetic resonance imaging.  It is fast becoming more available. There is no radiation involved with MRI. Again, only certain organs are suitable for this modality at this time. 

Nuclear medicine: as the name suggests, these tests require injection of a radioactive substance into your blood stream in order to evaluate an organ. It is safe, however there are certain groups of people who should generally not have these tests e.g. pregnant women.