Intelligent metasurfaces have demonstrated great promise in revolutionizing wireless communications. One notable example is the two-dimensional (2D) programmable metasurface, which is also known as reconfigurable intelligent surfaces (RIS) to manipulate the wireless propagation environment to enhance network coverage. More recently, three-dimensional (3D) stacked intelligent metasurfaces (SIM) have been developed to substantially improve signal processing efficiency by directly processing analog electromagnetic signals in the wave domain. Another exciting breakthrough is the flexible intelligent metasurface (FIM), which possesses the ability to morph its 3D surface shape in response to dynamic wireless channels and thus achieve diversity gain. In this paper, we provide a comprehensive overview of these emerging intelligent metasurface technologies. We commence by examining recent experiments of RIS and exploring its applications from four perspectives. Furthermore, we delve into the fundamental principles underlying SIM, discussing relevant prototypes as well as their applications. Numerical results are also provided to illustrate the potential of SIM for analog signal processing. Finally, we review the state-of-the-art of FIM technology, discussing its impact on wireless communications and identifying the key challenges of integrating FIMs into wireless networks.