It depends on where you live, the regulations, and what sort of arrangement the demolition company had with the waste removal company. Waste removal is usually handled by a contractor, not the demolition company themselves.
Some of the waste left behind after a building is demolished may be toxic. Common toxic materials found in this situation include lead, mercury, and asbestos. These, of course, have to be disposed of following local laws. They often end up in special landfills made to contain the potential for environmental contamination.
The bulk of the waste, however, is made out of recyclable material. Metal, glass, wood, and even concrete are all recyclable. The latter is often crushed into concrete aggregate, making it useful again.
You have likely already stepped on recycled concrete yourself. Concrete aggregate can be used to make walkways, driveways, and other outdoor heavy surfaces. With the benefit of being permeable, allowing rainwater to filter through to the soil below.