These very cool flies, who can hover in a single spot and seem to defend aerial territories can do many other cool things. They remember their aerial spots using landmark cues and can return to almost exactly the same spot with accuracies in the mm range.
But by far the coolest thing (if they can do it, it has been proved yet) is motion camouflage. Male hoverflies apparently seem to sneak up on females during mating flights using this trick. The trick is to appear like a stationary object on the retina of the pursued while actually moving closer to it. The eyes of many insects are not quite resolved well enough and an object has to get very close to them before the size is perceivably larger and by the this time the pursuing insect is close enough to 'attack'. Now if the pursued animal was stationary this is straightforward. You just keep moving in a straight line towards it, not making any lateral movements with respect to it.
However if it is moving, you need to calculate where you ought to be in its field of vision and be there. The diagram above shows what this task would be like. (taken from Andersen and McOwan, (2003), they have a neat computational model of this behaviour) So you need to be able some kind of prediction about what its doing, apart from having the motor skills needed to compensate by moving as well. Hoverflies like this one appear to have all the requirements and apparently so do the coolest insect predators, the dragonflies.