There are a variety of composting options which all accomplish the same task of breaking down organic material into a rich, soil amendment. Composting can be done in:
Bins
Piles
Pits
Trenches
Tumblers
The use of worms, cover crops or sheet composting
Bins & Tumblers
Bins and / or tumblers come in a variety of different shapes and forms, and are made from numerous materials including:
Chicken wire
Garbage cans
Old lumber
Pallets
Plastics
PVC
Rain barrels
Snow fences
Any other material one has access to
Bins are often preferred in urban settings, because they keep compost neat and tucked away while providing heat and moisture retention, but piles are generally easier to access and maintain. Compost tumblers are also available, and these overcome the potential maintenance challenges of bins, but are generally expensive and don't have the benefit of keeping your compost in contact with the ground, which is a source of useful organisms vital in the role or decomposition.