The growing interest in near-infrared (NIR) imaging is explained by the increasing number of applications in this spectral range, which includes process monitoring and medical imaging. NIR-to-visible optical upconverters made by integrating a NIR photosensitive unit with a visible emitting unit convert incident NIR light to visible light, allowing imaging of a NIR scene directly with the naked eye. Optical upconverters made entirely from organic and hybrid materials - which include colloidal quantum dots, and metal-halide perovskites - enable low-cost and pixel-free NIR imaging. These devices have emerged as a promising addition to current NIR imagers based on inorganic semiconductor photodiode arrays interconnected with read-out integrated circuitry. Here, we review the recent progress in the field of optical upconverters made from organic and hybrid materials, explain their functionality and characterization, and identify open challenges and opportunities.