In manufacturing conventional camera lens elements, each surface is shaped by rubbing it against the face of a tool having a complementary curve, grinding away glass using progressively finer abrasives. This motion of lens blank against tool automatically generates a surface which is a section of a sphere—any deviations from that curve will be ground away. Thus, all the classic lens designs used during photography's first century used spherical lens surfaces exclusively.
However the possibility of non-spherical surfaces was long understood to permit better aberration correction, potentially even reducing the total number of lens elements required. In astronomical optics, the primary mirror of many reflecting telescopes is hand-figured to a parabolic curve; and by 1930 Bernhard Schmidt had produced a telescopic camera with an f/1.75 focal ratio, using a glass "corrector plate" hand-figured with a complex aspheric surface.
With modern software, it is quite possible for a lens designer to compute the shape of arbitrarily-curved lens surfaces; but for many years these curves could only be produced through hand polishing and trial-and-error testing. Such products were inevitably exotic and expensive. The breakthrough came with advances in molding technology (often using optically-clear plastics); and by the early 2000s aspherical elements were a standard feature of many lens designs, even in such budget-conscious markets as phonecams and pocket point-and-shoots.