The rapid advancement of wireless communication technologies has precipitated an unprecedented demand for high data rates, extremely low latency, and ubiquitous connectivity. In order to achieve these goals, stacked intelligent metasurfaces (SIM) has been developed as a novel solution to perform advanced signal processing tasks directly in the electromagnetic wave domain, thus achieving ultra-fast computing speed and reducing hardware complexity. This article provides an overview of the SIM technology by discussing its hardware architectures, advantages, and potential applications for wireless sensing and communication. Specifically, we explore the utilization of SIMs in enabling wave-domain beamforming, channel modeling and estimation in SIM-assisted communication systems. Furthermore, we elaborate on the potential of utilizing a SIM to build a hybrid optical-electronic neural network (HOENN) and demonstrate its efficacy by examining two case studies: disaster monitoring and direction-of-arrival estimation. Finally, we identify key implementation challenges, including practical hardware imperfections, efficient SIM configuration for realizing wave-domain signal processing, and performance analysis to motivate future research on this important and far-reaching topic.