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 propose the concept of a dynamic scattering array (DSA) as a versatile 3D structure capable of performing joint wave-based computing and radiation by moving the processing from the digital domain to the electromagnetic (EM) domain. We provide a general analytical framework for modeling DSAs, introduce specific design algorithms, and apply them to various use cases. The examples presented in the numerical results demonstrate the potential of DSAs to further 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.