The development of metasurfaces has unlocked various use cases in wireless communication networks to improve performance by manipulating the propagation environment. Intelligent omni-surface (IOS), an innovative technique in this category, is proposed for coverage extension. In contrast to the widely studied reflective metasurfaces, i.e., intelligent reflecting surfaces (IRSs), which can only serve receivers located on the same side of the transmitter, the IOS can achieve full-dimensional wireless communications by enabling the simultaneous reflection and refraction of the surface, and thus users on both sides can be served. In this paper, we provide a comprehensive overview of the state-of-the-art in IOS from the perspective of wireless communications, with the emphasis on their design principles, channel modeling, beamforming design, experimental implementation and measurements, as well as possible applications in future cellular networks. We first describe the basic concepts of metasurfaces, and introduce the corresponding design principles for different types of metasurfaces. Moreover, we elaborate on the reflective-refractive model for each IOS element and the channel model for IOS-aided wireless communication systems. Furthermore, we show how to achieve full-dimensional wireless communications with the IOS for three different scenarios. In particular, we present the implementation of an IOS-aided wireless communication prototype and report its experimental measurement results. Finally, we outline some potential future directions and challenges in this area.