Empowered by the latest progress on innovative metamaterials/metasurfaces and advanced antenna technologies, holographic multiple-input multiple-output (H-MIMO) emerges as a promising technology to fulfill the extreme goals of the sixth-generation (6G) wireless networks. The antenna arrays utilized in H-MIMO comprise massive (possibly to extreme extent) numbers of antenna elements, densely spaced less than half-a-wavelength and integrated into a compact space, realizing an almost continuous aperture. Thanks to the expected low cost, size, weight, and power consumption, such apertures are expected to be largely fabricated for near-field communications. In addition, the physical features of H-MIMO enable manipulations directly on the electromagnetic (EM) wave domain and spatial multiplexing. To fully leverage this potential, near-field H-MIMO channel modeling, especially from the EM perspective, is of paramount significance. In this article, we overview near-field H-MIMO channel models elaborating on the various modeling categories and respective features, as well as their challenges and evaluation criteria. We also present EM-domain channel models that address the inherit computational and measurement complexities. Finally, the article is concluded with a set of future research directions on the topic.