  Reconfigurable intelligent surfaces (RIS) are passive controllable arrays of
small reflectors that direct electromagnetic energy towards or away from the
target nodes, thereby allowing better management of signals and interference in
a wireless network. The RIS has the potential for significantly improving the
performance of wireless networks. Unfortunately, RIS also multiplies the number
of Channel State Information (CSI) coefficients between the transmitter and
receiver, which magnifies the challenges in estimating and communicating the
channel state information. Furthermore, the simplicity and cost-effectiveness
of the passive RIS also implies that the incoming links are not locally
estimated at the RIS, and fresh pilots are not inserted into outgoing RIS
links. This introduces new challenges for training and estimation of channel
state information. The rapid growth of the literature on CSI acquisition in
RIS-aided systems has been accompanied by variations in the underlying
assumptions, models, and notation, which can obscure the similarities and
differences of various techniques, and their relative merits. This paper
presents a comprehensive exposition of principles and approaches in RIS channel
estimation. The basic ideas underlying each class of techniques are reduced to
their simplest form under a unified model and notation, and various approaches
within each class are discussed. Several open problems in this area are
identified and highlighted.
