Radioactive material needs long-term storage as encased in glass. Siting is a real problem as no one wants a toxic waste dump near their area. Another type is to make mounds separated by barriers. This is a better model where the water table is high. An extraordinary example of a landfill is the Freshkills land fill on Staten Island.
Hazardous waste is sited above ground or in specially constructed dikes or trenches.
Methane gas seeps from rotting organic matter. It needs to be trapped and burned off. The ideal site has little if any ground water, impermeable bed rock or bentonite clay. Low amounts of surface water or rain. Organic solvents are 100x more permeable in clay than water .