A review is presented of previous papers on the apparent shape of bodies travelling with speeds comparable to that of light. It is shown that the visibility or otherwise of the Lorentz contraction depends on the method of observation adopted and on the shape of the body in question. Visual, photographic and radar-type methods are discussed, including the hitherto neglected application of stereoscopic perception. The theory is developed for a new possible technique of observation, that in which an object illuminates itself momentarily in its rest frame, the image being recorded as a time exposure by the observer.