Measurements of soft X-ray emission from the JET plasma have been analysed with tomographic reconstruction methods. Because there are two detector arrays, two-dimensional images of X-ray emissivity are obtained without having to resort to rotation models. Several algorithms are employed in order to get as much detail as possible in the images while keeping any guiding assumptions to a minimum. The data analysed so far have been used principally to study MHD instabilities, and illustrative examples of the sawtooth crash and of disruptions are described.