  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 are not from the 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.
