With the rapid development of computational electromagnetic theories and methods, it is now possible to study accurately and quantitatively the basic physical principle and rules of interaction between electromagnetic waves and complicated targets/environment through numerical methods. Such numerical modeling and theoretical prediction can lay a solid foundation and inspire innovative ideas for the research and development of new technologies in the fields of target detection and identification in a complex environment, exploration of underground resources, information acquisition in a ground-air or ocean-air environment, electromagnetic stealth design, electromagnetic countermeasures, etc. The study and application of accurate and efficient numerical modeling tools will remarkably promote the research and development of relevant technologies. In this article, we first review the research background and scientific problems in the interaction of electromagnetic waves and targets/environment. Next, we focus on the introduction of theoretical modeling and numerical methods for the composite scattering of targets in a half-space environment, the state-of-the-art development of half-space Greens function and its efficient computation, integral equation methods, and fast algorithms. Finally, we propose several key research topics and areas for the interaction of electromagnetic waves and targets/environment, including composite scattering model and numerical methods for targets in a high-contrast half space; highly efficient analysis of electrically large targets in a half space; approximation models for analyzing composite scattering; accuracy study and comparison of full-wave numerical and high-frequency or ray methods in a half space; combination of stochastic time-varying model of the rough ground/sea surface and the deterministic half-space model, rules and adaptivity (for example, the differential RCS of targets in a half space and the random scattering of rough surfaces as additive noise); numerical models of composite scattering in a half space for sensor applications; spatial selection and adaptive focusing in the low-frequency near-field detection in a layered medium; and verification, validation, and evaluation of numerical models in a large-scale electromagnetic computation.