Ionized gases containing fine (μm to sub-μm sized) charged dust grains, referred to as dusty plasmas, occur in diverse cosmic and laboratory environments. Dust occurs in many space and astrophysical environments, including planetary rings, comets, the Earth's ionosphere, and interstellar molecular clouds. Dust also occurs in laboratory plasmas, including processing plasmas, and crystallized dusty plasmas. Charged dust can lead to various effects in a plasma. In this review, some physical processes in dusty plasmas are discussed, with an emphasis on applications to dusty plasmas in space. This includes theoretical work on several wave instabilities, the role of dust as an electron source, and Coulomb crystals of positively charged dust.