To meet the stringent requirements of next-generation wireless networks, multiple-input multiple-output (MIMO) technology is expected to become massive and pervasive. Unfortunately, this could pose scalability issues in terms of complexity, power consumption, cost, and processing latency. Therefore, novel technologies and design approaches, such as the recently introduced holographic MIMO paradigm, must be investigated to make future networks sustainable. In this context, we investigate the concept of a dynamic scattering array (DSA) as a versatile electromagnetic (EM) structure capable of performing joint wave-based computing and radiation by moving the processing from the digital domain to the EM domain. We provide a general, wideband analytical framework for modeling the DSA, which includes a power matching network and realistic reconfigurable loads. Then we introduce specific design algorithms, and apply them to various use cases. We demonstrate that some recent EM processing structures can be seen as particular cases of our general framework. The examples presented in the numerical results corroborate the potential of DSAs to reduce complexity and the number of radiofrequency (RF) chains in holographic MIMO systems while achieving enhanced EM wave processing and radiation flexibility for tasks such as beamforming and single- and multi-user MIMO, also exhibiting superdirectivity capabilities.