Reconfigurable intelligent surfaces (RIS) constitute a revolutionary technique of beneficially reconfiguring the smart radio environment. However, despite the fact that wireless propagation is of time-varying nature, most of the existing RIS contributions focus on time-invariant scenarios for the following reasons. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Firstly</i> , it becomes impractical to instantaneously feed back the control signal based on the doubly selective non-line-of-sight (NLoS) fading scenario. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Secondly</i> , channel estimation conceived for the high-mobility and high-dimensional RIS-assisted links has to take into account the spatial-domain (SD), time-domain (TD), and frequency-domain (FD) correlations imposed by the angle-of-arrival/departure (AoA/AoD), the Doppler and the orthogonal frequency-division multiplexing (OFDM) operations, respectively, where none of the existing solutions can be directly applied. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Thirdly</i> , it is far from trivial to maximize the NLoS channel powers on all subcarriers by a common set of RIS reflecting coefficients. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Fourthly</i> , in the face of double selectivity, it becomes inevitable to encounter either inter-symbol interference (ISI) or inter-channel interference (ICI) during the signal detection in the TD or in the FD, respectively. Against this background, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">firstly</i> , we focus our attention on line-of-sight (LoS) dominated unmanned aerial vehicle (UAV) scenarios. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Secondly</i> , we conceive new minimum mean squared error (MMSE) channel estimation methods for doubly selective fading, which perodically transmit pilot symbols embedded into the TD and FD over the SD in order to beneficially exploit the correlations in the three domains. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Thirdly</i> , the RIS coefficients are optimized by a low-complexity algorithm based on the LoS representation of the end-to-end system model. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Fourthly</i> , tailor-made interference cancallation techniques are devised for improving the signal detection both in the FD and in the TD. Our simulation results are examined in six frequency bands licensed in 5 G, which confirms that the employment of RIS is capable of achieving substantial performance improvements.