Detection of neutrons, at high total efficiency, with greater resolution in kinetic energy, time and/or real-space position, is fundamental to the advance of subfields within nuclear medicine, high-energy physics, non-proliferation of special nuclear materials, astrophysics, structural biology and chemistry, magnetism and nuclear energy. Clever indirect-conversion geometries, interaction/transport calculations and modern processing methods for silicon and gallium arsenide allow for the realization of moderate- to high-efficiency neutron detectors as a result of low defect concentrations, tuned reaction product ranges, enhanced effective omnidirectional cross sections and reduced electron-hole pair recombination from more physically abrupt and electronically engineered interfaces. Conversely, semiconductors with high neutron cross sections and unique transduction mechanisms capable of achieving very high total efficiency are gaining greater recognition despite the relative immaturity of their growth, lithographic processing and electronic structure understanding. This review focuses on advances and challenges in charged-particle-based device geometries, materials and associated mechanisms for direct and indirect transduction of thermal to fast neutrons within the context of application. Calorimetry- and radioluminescence-based intermediate processes in the solid state are not included.