An X-ray tube includes an evacuated envelope; a cold cathode mounted at one end of the envelope and capable of field emission of electrons when subjected to a high electrostatic field; and an anode mounted at the opposite end of the envelope coaxial with and axially spaced from the cathode, and capable of emitting X-rays when struck by electrons emitted by the cathode. The envelope includes an end wall made of thermally-conductive and electrically-insulating material in contact with the anode and formed with a fluid cooling channel to remove the heat generated at the anode. In one described embodiment, the cathode includes a body of a getter material which is both electron emissive and gas absorptive. In other described embodiments, the cathode includes a carbon nanotube field-emission electron source.