  After the {\em Solar and Heliospheric Observatory} ({\em SOHO}) was launched
in 1996, the aboard Extreme Ultraviolet Imaging Telescope (EIT) observed a
global coronal wave phenomenon, which was initially named "EIT wave" after the
telescope. The bright fronts are immediately followed by expanding dimmings. It
has been shown that the brightenings and dimmings are mainly due to plasma
density increase and depletion, respectively. Such a spectacular phenomenon
sparked long-lasting interest and debates. The debates were concentrated on two
topics, one is about the driving source, and the other is about the nature of
this wavelike phenomenon. The controversies are most probably because there may
exist two types of large-scale coronal waves that were not well resolved before
the {\em Solar Dynamics Observatory} ({\em SDO}) was launched: one is a
piston-driven shock wave straddling over the erupting coronal mass ejection
(CME), and the other is an apparently propagating front, which may correspond
to the CME frontal loop. Such a two-wave paradigm was proposed more than 13
years ago, and now is being recognized by more and more colleagues. In this
paper, we review how various controversies can be resolved in the two-wave
framework and how important it is to have two different names for the two types
of coronal waves.
