An electron that completes a transition deep inside an atom now started its motion some tens to thousands of attoseconds before. 
This motion can therefore be most conveniently measured in units of attoseconds just as macroscopic phenomena are  
naturally clocked in seconds. In the microscopic world of electrons (attoworld for short) motion is speeded up so 
immensely that the respective time unit makes the period of a heart beat (~10¹⁸ attoseconds,
see wordinfo and wikipedia) appear to be stretched beyond the age of the universe 
(~5x10¹⁷ seconds). This is evident from the accompanying time scale,
on which a step  represents a thousandfold time expansion
(upwards)  or shortening (downwards). 

How could we possibly control the 
hyperfast motion of electrons, the fastest 
outside the atomic core, how could it be tracked and 
visualised in slow-motion replay, and why should we bother?