The storage of volatile and semivolatile species in Hanford Site waste, their transport through any overburden of waste to the tank headspaces, the physical phenomena affecting their concentrations in the headspaces, and their eventual release into the atmosphere above the tanks are examined. The physical and chemical phenomena that cause and influence the transport of gases and vapors from within the waste to the tank headspaces are described, and available supporting evidence from tank observations are provided. Key findings are that the rate that volatile species from within the waste are transported to the tank headspaces is limited by its transport through the interstitial liquid. Transport through convective liquids (e.g., a liquid pool), through drained porous solids and through the boundary layer of the headspace itself is rapid compared to the rate that species migrate through interstitial liquids. Nonpolar organic compounds do not diffuse through aqueous wastes as rapidly as polar species, and their transport may be governed by the rate they are carried to the surface with rising gas bubbles. The inventory of waste in trapped gas bubbles is probably only important for hydrogen, nitrous oxide, and methane. Headspace concentrations for most species are determined by the balance between the rate they are released by the waste and the rate they are removed via the ventilation system. Headspaces are convectively mixed by temperature differences between the waste surface and the tank dome. Vapor condensation in the headspace, either on the dome and walls or as an aerosol, can cause the absorption of soluble species (e.g., ammonia in water condensate) diminishing the concentrations of soluble species both in the headspace and in air released to the atmosphere. Passive ventilation is thought to be due to barometric pressure fluctuations, a difference between temperature of the ambient air and the headspace (the chimney effect), and the effects of wind on risers, pits, and instruments that are connected to the tank headspace (or to connected tanks). Passive ventilation rates vary significantly from tank to tank and from one time period to another. Higher passive ventilation rates appear to be associated with multiple and larger ventilation pathways. Headspace composition varies with a variety of factors that tend to be tank-specific, and no simple relationship between seasonal changes in the tank conditions and headspace compositions has been identified.