Hi, Bill -- Each aspheric surface used in a lens potentially can result in one less whole element being necessary, and/or that abberations can be better corrected, especially at wide apertures.
Fewer elements often results in less internal flare, better contrast, and potentially smaller and lighter. But I think most lens makers take advantage of one or more aspheric surfaces to improve performance.
In conjunction with asph surfaces, current designers seem to often use moving elements or groups that shift position in focusing to improve close-up performance and then construct the lens to focus closer.
The better correction of optical abberations seems to have the side effect of making out-of-focus areas somewhat less pleasant. So some avoid asph lenses in pursuit of the 'classical' aesthetic. 🙂