Reconfigurable intelligent surfaces (RISs) enable programmable control of wireless propagation. Beyond environmental deployments, integrating metasurfaces at the antenna front end allows direct manipulation of the radiated electromagnetic field and enables wave-domain signal processing. In this context, stacked intelligent metasurfaces (SIMs) have recently been proposed as an advanced architecture in which multiple programmable metasurface layers interact through wave propagation, enabling richer and more flexible electromagnetic transformations than conventional single-layer designs. By leveraging cascaded wave-matter interactions at the transmitter or receiver front end, SIMs substantially expand the design space of programmable wireless systems. This survey provides a comprehensive overview of SIMs technologies from the electromagnetic processing perspective, covering their physical principles, modeling frameworks, hardware realizations, and emerging architectural designs. We review existing modeling approaches based on cascaded operators, multiport impedance formulations, and network parameter representations, and discuss their implications for scalable optimization and system design. The survey further examines key communication functionalities enabled by front-end metasurface processing, including communication performance optimization, near-field and wideband transmission, learning-driven control, integrated sensing and communications, and emerging architectures such as cell-free and non-terrestrial networks. Finally, we identify open research problems related to physical modeling, scalability, hardware-algorithm co-design, and network integration, and outline promising directions toward realizing SIM-based antenna front ends as fully programmable electromagnetic processors for future sixth-generation (6G) wireless systems.