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The purpose of this article is to investigate the so-called "near-field reactive" or "very-near-field" region of radiating apertures with different shapes and aperture illuminations. In this unusual and rather unknown region, we underline the specific behavior of the radiated fields, the wave impedance, and the power density. Thanks to these properties, we succeed in. determining, in the first part, the outer boundary of the "very-near-field" region of a circular aperture with a uniform illumination law. Then, we review the influence of the illumination law and of the aperture shape on the extent of this region, through the cases of parabolic or cosine laws, and the case of square-shaped aperture. This study can find various applications in the wireless communications and radar antenna domains and, more recently, in electromagnetic compatibility problems.