This chapter starts with the state-of-the-art technology of the intelligent reflecting surface (IRS) which is emerged as a promising new paradigm to achieve smart and reconfigurable wireless propagation environment for beyond fifth-generation (B5G)/sixth-generation (6G) wireless communication systems. The motivation as well as the research background of the IRS is first presented. Then, the potential applications of the IRS in wireless information transmission and wireless energy transmission are highlighted and discussed. The unique property of IRS as well as its difference compared to the other technologies are studied. Next, we introduce the fundamental signal processing technique for IRS to show how it works. In addition, several types of IRS hardware architectures and hardware constraints are introduced and compared. Through the discussion, it is revealed that the IRS can provide significant high passive beamforming gain by adjusting its phase shifts, which motivates the main theme of this monograph.