Some removals require the use of a crane. This can be for a number of reasons; tree size and shape, location, condition of the tree, other surrounding structures or time constraints. Here is a timelapse video of a removal using a 40 tonne slew crane in Maitland.
The most cost-effective way to remove tree stumps and roots is to grind them using a machine, appropriately named a stump grinder. This eliminates the effort of trying to dig the stump out (much harder than it looks), then take the stump to land fill and buy soil to fill the hole. Using a stump grinder turns the stump into mulch which is then used to fill the hole.