Using nanowires for photodetection constitutes an opportunity to enhance the absorption efficiency while reducing the electrical cross-section of the device. They present interesting features like compatibility with silicon substrates, which offers the possibility of integrating detector and readout circuitry, and facilitates their transfer to flexible substrates. Within a nanowire, it is possible to implement axial and radial (coreshell) heterostructures. These two types can be combined to obtain three-dimensional carrier confinement (dot-in-a-wire). The incorporation of heterostructures in nanowire photodetectors opens interesting opportunities of application and performance improvement. Heterojunctions or type-II heterostructures favor the separation of the photogenerated electrons and holes, and the implementation of quantum dots in a nanowire can be applied to the development of quantum photodetectors. This paper provides a general review of latest progresses in nanowire photodetectors, including single nanowires and heterostructured nanowires.