  A major, albeit serendipitous, discovery of the SOlar and Heliospheric
Observatory mission was the observation by the Extreme Ultraviolet Telescope
(EIT) of large-scale Extreme Ultraviolet (EUV) intensity fronts propagating
over a significant fraction of the Sun's surface. These so-called EIT or EUV
waves are associated with eruptive phenomena and have been studied intensely.
However, their wave nature has been challenged by non-wave (or pseudo-wave)
interpretations and the subject remains under debate. A string of recent solar
missions has provided a wealth of detailed EUV observations of these waves
bringing us closer to resolving their nature. With this review, we gather the
current state-of-art knowledge in the field and synthesize it into a picture of
an EUV wave driven by the lateral expansion of the CME. This picture can
account for both wave and pseudo-wave interpretations of the observations, thus
resolving the controversy over the nature of EUV waves to a large degree but
not completely. We close with a discussion of several remaining open questions
in the field of EUV waves research.
