Sponging mouthparts consist of a fleshy, elbowed labium, at the distal end of which are large, sponge-like organs called the labella (singular, labellum). The labella is a complex structure consisting of many grooves, called pseudotrachea, which sops up liquids much like a sponge does. Salivary secretions from the labella assist in dissolving and collecting food particles so that they may be more easily taken up by the pseudotrachea (this is thought to occur by capillary action). The liquid food is then drawn up from the pseudotracheae through the food channel into the esophagus. The SEM photograph above shows the fly labella, the two lobes of which can be easily distiguished, along with the pseudotrachea, which are also clearly visible.
Flies with sponging mouthparts are usually incapable of biting, however some species have sharp teeth on the pseudotracheae to rasp flesh and draw up blood e.g. the tsetse fly.
The 'higher' flies, i.e. houseflies and their relatives, have essentially lost the mandibles and maxillae, with the maxillary palpi being all that remains of these appendages. The labrum (not shown in the diagram) is located between the maxillary palps.
SEM photo courtesy of Kevin McKenzie, Electron Microscopy Unit, Department of Zoology, University of Aberdeen http://www.abdn.ac.uk/~nhi691/