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As ubiquitous wireless communication becomes part of life, the demand on antenna miniaturization and interference reduction becomes more extreme. However, antenna size and performance are limited by radiation physics, not technology. In order to understand antenna radiation and energy storage mechanisms, classical and alternative viewpoints of radiation are discussed. Unlike the common sense of classical antenna radiation, it is shown that the entire antenna fields contribute to both radiation and energy storage with varying total energy velocity during the radiation process. These observations were obtained through investigating impedance, power, the Poynting vector, and energy velocity of a radiating antenna. Antenna transfer functions were investigated to understand the real-world challenges in antenna design and overall performance. An extended model, using both the singularity expansion method and spherical mode decomposition, is introduced to analyze the characteristics of various antenna types including resonant, frequency-independent, and ultra-wideband antennas. It is shown that the extended model is useful to understand real-world antennas. Observations from antenna radiation physics and transfer function modeling lead to both corrections and extension of the classical fundamental-limit theory on antenna size. Both field and circuit viewpoints of the corrected limit theory are presented. The corrected theory is extended for multi-mode excitation cases and also for ultra-wideband and frequency-independent antennas. Further investigation on the fundamental-limit theory provides new innovations, including a low-Q antenna design approach that reduces antenna interference issues and a generalized approach for designing an antenna close to the theoretical-size limit. Design examples applying these new approaches with simulations and measurements are presented. The extended limit theory and developed antenna design approaches will find many applications to optimize compact antenna solutions with reduced near-field interactions. / Ph. D.