Observations with EUVE, ROSAT, and BeepoSAX have shown that some clusters of galaxies produce intense EUV emission. These findings have produced considerable interest; over 100 papers have been published on this topic in the refereed literature. A notable suggestion as to the source of this radiation is that it is a 'warm' (106 K) intracluster medium which, if present, would constitute the major baryonic component of the universe. A more recent variation of this theme is that this material is 'warm-hot' intergalactic material condensing onto clusters. Alternatively, inverse Compton scattering of low energy cosmic rays against cosmic microwave background photons has been proposed as the source of this emission. Various origins of these particles have been posited, including an old (${\~}$ 수식 이미지Giga year) population of cluster cosmic rays; particles associated with relativistic jets in the cluster; and cascading particles produced by shocks from sub-cluster merging. The observational situation has been quite uncertain with many reports of detections which have been subsequently contradicted by analyses carried out by other groups. Evidence supporting a thermal and a non-thermal origin has been reported. The existing EUV, FUV, and optical data will be briefly reviewed and clarified. Direct observational evidence from a number of different satellites now rules out a thermal origin for this radiation. A new examination of subtle details of the EUV data suggests a new source mechanism: inverse Compton scattered emission from secondary electrons in the cluster. This suggestion will be discussed in the context of the data.