This thesis concerns the interaction of small, particulate, solid matter - 'dust' - with plasmas, in the plasma edge region where such dust is commonly found. Dust in this region can have a significant impact on a variety of industrial plasma applications, and it is low-temperature industrial plasmas that form the focus of this work. A novel model for the sheath region at the edge of a plasma is proposed, to account for the loss of electrons at the plasma boundary. This is then compared to an existing Boltzmann electron model; significant differences are noted in the sheath structure, and consequently the charging and dynamics of dust in the plasma sheath. The effect of sparse ion collisions in the vicinity of a dust grain near the plasma edge is also investigated. The strong plasma flow in the edge region is found to significantly increase collisional charging of dust grains. Somewhat counter-intuitively, it is found that even sparse collisions can play a significant (and in fact dominant) role in the charging and shielding of dust grains at the edge of a plasma. The length-scale over which the charge on such grains is shielded by the plasma is found to be significantly less than the Debye length. Together, the altered grain charging and shielding behaviour have the potential to fundamentally alter how dust grains interact with edge-plasmas.