Neutral beam injection is one of the most important methods of plasma heating in thermonuclear fusion experiments, allowing the attainment of fusion conditions as well as driving the plasma current. Neutral beams are generally produced by electrostatically accelerating ions, which are neutralised before injection into the magnetised plasma. At the particle energy required for the most advanced thermonuclear devices and particularly for ITER, neutralisation of positive ions is very inefficient so that negative ions are used. The present paper is devoted to the description of the phenomena occurring when a high-power multi-ampere negative ion beam travels from the beam source towards the plasma. Simulation of the trajectory of the beam and of its features requires various numerical codes, which must take into account all relevant phenomena. The leitmotiv is represented by the interaction of the beam with the background gas. The main outcome is the partial neutralisation of the beam particles, but ionisation of the background gas also occurs, with several physical and technological consequences. Diagnostic methods capable of investigating the beam properties and of assessing the relevance of the various phenomena will be discussed. Examples will be given regarding the measurements collected in the small flexible NIO1 source and regarding the expected results of the prototype of the neutral beam injectors for ITER. The tight connection between measurements and simulations in view of the operation of the beam is highlighted. operating in the existing tokamaks. Consequently, PRIMA, the ITER Neutral Beam Test Facility [2], was set up to constitute a test-bed, where the solutions to all the issues related to the achievement of full performances in the heating NBI system for ITER are going to be addressed and optimised, particularly regarding critical aspects like density and uniformity of the extracted negative ion current, high voltage holding and heat loads on the components [3]. Megavolt ITER Injector Concept Advancement (MITICA) is the full-scale prototype of the ITER NBIs [4]; it includes an RF-driven plasma source for the production of negative ions and should operate at a pressure as low as 0.3 Pa in hydrogen or deuterium gasses. The negative ions are produced on the surface of the grid (Plasma Grid, PG) that closes the plasma region; their production is enhanced thanks to a thin caesium layer continuously deposited over the PG by evaporation. Negative ions are extracted through the 1280 apertures in the PG by application of a suitable positive voltage to the extraction grid (EG), located just downstream of the PG. The RF plasma source operates at an applied electric potential of about −1 MV. Five additional acceleration grids (AG1, AG2, AG3, AG4, GG), at intermediate electric potential increasing by 200 kV steps, are located downstream with respect to the EG, thus constituting a 5-stage electrostatic accelerator. The resulting negative ion beam at 1 MeV, after passing through a gas cell neutraliser and an electro...