A warm/hot dust component (at temperature $>$ 300K) has been detected around $\sim$ 20% of stars. This component is called "exozodiacal dust" as it presents similarities with the zodiacal dust detected in our Solar System, even though its physical properties and spatial distribution can be significantly different. Understanding the origin and evolution of this dust is of crucial importance, not only because its presence could hamper future detections of Earth-like planets in their habitable zones, but also because it can provide invaluable information about the inner regions of planetary systems. In this review, we present a detailed overview of the observational techniques used in the detection and characterisation of exozodiacal dust clouds ("exozodis") and the results they have yielded so far, in particular regarding the incidence rate of exozodis as a function of crucial parameters such as stellar type and age, or the presence of an outer cold debris disc. We also present the important constraints that have been obtained, on dust size distribution and spatial location, by using state-of-the-art radiation transfer models on some of these systems. Finally, we investigate the crucial issue of how to explain the presence of exozodiacal dust around so many stars (regardless of their ages) despite the fact that such dust so close to its host star should disappear rapidly due to the coupled effect of collisions and stellar radiation pressure. Several potential mechanisms have been proposed to solve this paradox and are reviewed in detail in this paper. The review finishes by presenting the future of this growing field.