  Channel reciprocity greatly facilitates downlink precoding in time-division
duplexing (TDD) multiple-input multiple-output (MIMO) communications without
the need for channel state information (CSI) feedback. Recently, reconfigurable
intelligent surfaces (RISs) emerge as a promising technology to enhance the
performance of future wireless networks. However, since the artificial
electromagnetic characteristics of RISs do not strictly follow the normal laws
of nature, it brings up a question: does the channel reciprocity hold in
RIS-assisted TDD wireless networks? After briefly reviewing the reciprocity
theorem, in this article, we show that there still exists channel reciprocity
for RIS-assisted wireless networks satisfying certain conditions. We also
experimentally demonstrate the reciprocity at the sub-6 GHz and the
millimeter-wave frequency bands by using two fabricated RISs. Furthermore, we
introduce several RIS-assisted approaches to realizing nonreciprocal channels.
Finally, potential opportunities brought by reciprocal/nonreciprocal RISs and
future research directions are outlined.
