Male blowflies chase and catch other flies in fast acrobatic flights. To unravel the underlying control system, I presented a black moving sphere instead of a real fly as pursuit target. By varying the size and speed of the target, this paradigm allowed a systematic analysis of the decisive visual determinants that guide chasing behaviour. Chasing male flies adjust their forward velocity depending on the retinal size of the target, suggesting that retinal size is a relevant input variable of the control system. The chasing fly focuses the target with great accuracy in the frontal part of its visual field by means of a smooth pursuit control system using the retinal position of the target to determine the flight direction. To test whether or not experimentally established hypotheses on the underlying control system are sufficient to explain chasing behaviour a virtual fly was simulated. Two operating instructions for steering the chasing virtual fly were derived from behavioural experiments: (i) The retinal size of the target controls the fly's forward speed and, thus, indirectly its distance to the target. (ii) A smooth pursuit system uses the retinal position of the target to regulate the fly's flight direction. Low-pass filters implement neuronal processing time. Treating the virtual fly as a point mass, its kinematics is modelled in consideration of the effects of translatory inertia and air friction. Despite its simplicity, the model shows behaviour similar to that of real flies. It is shown that the virtual fly does not only pursue smoothly moving artifical targets but also real flies flying on more complicated courses in a similar manner as do real flies.