My experience is with hangi or umu, the earth oven used by maori in NZ.
You start with a fire and stones - the stones need to hold heat without cracking or crumbling (river stones are right out - they can explode when the water in them expands). Fire-bricks or old railway brake shoes are a good modern alternative. Iron or steel gives up the heat too quickly and can burn the food.
Once the stones are hot, you rake them out of the fire into the pit, and cover with damp sacks. Then the trays of food are layered on, meat and kai moana (seafood - fish, clams, mussels, crayfish, lobster, abalone) first, then potatoes, kumara (sweet potato), pumpkin, puha (sow thistle), corn and other veges are put on, more damp sacks cover everything and then the whole lot is covered with dirt to stop the heat and steam escaping. Leave in the ground for several hours, lift and serve with rewena bread (potato based sourdough bread). Yum. 
The effect is to steam with pressure (up to 4 psi), roast with heat (300[sup]o[/sup]C), and trap the dripping juices on the hot rocks, producing distinctive flavour elements. A company in NZ spent years developing a commercial hangi cooking process for mass produced food that had the right flavour elements.
Kalua use an imu or umu, which is similar to a hangi. A clambake is the same, using stones or cannonballs, and seaweed instead of sacks.
I wonder if I could persuade the vicar to let me lay a hangi in the vicarage garden at the end of summer, as a church fundraiser. That would be a whole lot of fun, but leave him with a big hole in his lawn.
Si