Neuromorphic devices that emulate biological synaptic behavior are emerging as key enablers for in-sensor intelligence. While visible-light-responsive systems have dominated the field, recent efforts have expanded toward invisible spectral regions: ultraviolet (UV), infrared (IR), and X-ray, where unique photon-matter interactions offer new avenues for optical plasticity. These invisible-wavelength stimuli enable synaptic functions such as short-term and long-term potentiation through mechanisms like persistent photoconductivity, defect ionization, and interfacial charge trapping, often without the need for external programming circuitry. Although these devices are increasingly important for intelligent imaging, radiation-tolerant electronics, and secure communication, related studies are still fragmented across different fields and lack an organized overview. In this review, we systematically categorize and analyze optoelectronic synapses that operate under UV, IR, and X-ray illumination. We highlight representative material systems including Ga₂O₃, perovskites, wide-bandgap oxides, and hybrid nanocomposites, and discuss their device architectures, synaptic behaviors, and operational metrics. Special emphasis is placed on the underlying physical mechanisms, spectral selectivity, and integration prospects for artificial retinas, neuromorphic vision systems, and multimodal sensing arrays. We also provide outlooks for scalable, multispectral, and energy-efficient neuromorphic platforms beyond the visible.