Food Mill: A hand-cranked food mill purees soup by forcing ingredients through a preforated round disk to remove fibers, skins and seeds from vegetables. Most mills come with both medium and fine disks offering the cook a choice of coarser or smoother purees.
Food Processor: A food processor purees soups almost instantaneously. First, fit the processor with a metal blade. Ladle small batched of the cooked product and a bit of the liquid into the food processors bowl. Be careful not to over fill, fill to just about half way. Cover and pulse the machine several times, then process until the puree to desired consistency. When using a food processor, straining may be necessary to remove fibers, skins and seeds. Remove them by pouring contents into a sieve over large bowl or you may use a stainless steel wire mesh strainer.
Handheld blender ("Stick Blender"/"Immersion blender") Hand held blenders also called immersion blenders have a blade that can lowered directly into a pot of soup, blending large amounts of soup at one time without having to switch the contents from pot to a separate bowl. I prefer using an immersion blender for ease of use, less dishes to clean and for it's ability to easily achieve a smooth silky texture in soups in the least amount of time and with little effort. Immersion blenders also tend to incorporate air into the soup, resulting in a silky foamy texture.
Standing blender: Blenders make pureeing soups fast and easy, they can handle more liquid than food processors and usually produce a better puree than food processors. When using a blender, work in small batched and never fill blender more than half way to prevent overflow.