Methods for storing or disposing of nuclear waste include forming a drillhole that extends into the Earth from a terranean surface. The drillhole includes an entry at least proximate the terranean surface, a substantially vertical drillhole portion, and a hazardous material storage drillhole portion that is coupled to the substantially vertical drillhole portion and is formed in a subterranean salt formation. The methods further include moving a storage canister into the hazardous material storage drillhole portion. The storage canister is sized to fit from the drillhole entry through the substantially vertical drillhole portion, and into the hazardous material storage drillhole portion of the drillhole. The storage canister has an inner cavity that encloses nuclear waste material. The methods further include positioning a seal in the drillhole to isolate the hazardous material storage drillhole portion of the drillhole from the entry of the drillhole.