Reconfigurable intelligent surfaces (RISs) are regarded as a promising emerging hardware technology to improve the spectrum and energy efficiency of wireless networks by artificially reconfiguring the propagation environment of electromagnetic waves. Due to the unique advantages in enhancing wireless channel capacity, RISs have recently become a hot research topic. In this article, we focus on three fundamental physical-layer challenges for the incorporation of RISs into wireless networks, namely, channel state information acquisition, passive information transfer, and low-complexity robust system design. We summarize the state-of-the-art solutions and explore potential research directions. Furthermore, we discuss other promising research directions of RISs, including edge intelligence and physical-layer security.