The simplicity of synthesis of deterministically positioned inorganic semiconductor nanorods (NRs) and nanotubes (NTs) coupled with their chemical stability, high surface area, controllable optical properties and tunable surface functionality, have sparked worldwide research efforts towards biodiagnostic applications. Biosensors based on oriented and aligned one-dimensional (1-D) inorganic semiconductor nanostructures have demonstrated remarkable detection sensitivity, high throughput and label-free operability. In comparison to suspensions of nanoparticles and discrete randomly oriented nanowires, nanowire (NW) and nanotube arrays offer continuous charge transport pathways, a major advantage for all-electrical detection and in exploiting electrokinetic effects. We review highly sensitive biosensors based on oriented and aligned NTs/NRs/NWs employing conventional detection methods, inclusive of fluorescence, electrochemistry and electromechanical sensing as well as detection methods unique to nanowires such as field-effect transistors. Entirely new types of sensing applications such as the impaling of living cells to monitor cellular events in situ, and substrates with electrically controlled wetting for surface-assisted laser desorption and ionization are emerging to take advantage of the unique properties of nanowire arrays. Concurrently, we explain the semiconductor materials and architectures employed, and the functionalization procedures used to construct the biosensors. Aligned semiconductor array-based approaches are critically examined in relation to prevailing technologies to get a sense of the exclusive niches that nanotube/nanorod array biosensors inhabit. The versatility of the detection principles that nanowire/nanotube arrays are compatible with are enabling hybrid approaches where combinations of detection methods are used. Such advantages offset the complexity associated with changing the status quo with respect to the current state-of-the-art in biodiagnostic platforms and devices.