Many landfills are slowly closing down, there is only so many holes in the ground you can turn into hills anyway.
So modern burners are the way to go.
Many of the landfill sites have transfer stations where the waste is sorted, some still gets buried, some gets compressed and burnt,
some gets compressed and shipped to France and Germany, where they burn it for fuel generation.
The latest technology, is incredibly "clean burn" as it was explained to me, its something about recycling the burn and re-burning it.
The methane produced from landfills is turned into electricity on site, to power the site, the surplus is put back into the national grid.
The run off liquid is called leachate, (both from decomposing waste and rain fall passing through the landfill)
In its pure form is poisonous, that is taken away and processed I believe, but I know very little about that side of things.