Jupiter is one of the major targets for planetary exploration, and dust in the Jovian system is of great interest to researchers in the field of planetary science. In this paper, we review the five dust populations outside the ring system: grains in the region of the Galilean moons, potential dust from plumes on Europa, Jovian stream particles, particles in the outer region of the Jovian system ejected from the irregular satellites, and dust in the region of the Trojan asteroids. The physical environment for the dust dynamics is described, including the gravity, the magnetic field and the plasma environment. For each population, the dust sources are described, and the relevant perturbation forces are discussed. Observations and results from modeling are reviewed, and the distributions of the individual dust populations are shown. The understanding of the Jovian dust environment allows to assess the dust hazard to spacecraft, and to characterize the material exchange between the Jovian moons, their surface properties and distribution of non-icy constituents.