We summarise the reasons why aspheric surfaces, including non-rotationally-symmetric surfaces, are increasingly important to ground and space-based astronomical instruments, yet challenging to produce. We mainly consider the generic problem of producing aspheres, and then lightweight segments for the primary mirror of an Extremely Large Telescope. We remark on the tension between manufacturability of spherical segments, and performance with aspheric segments. This provides the context for our presentation of the novel Precessions process for rapid polishing and form-correction of aspheric surfaces. We outline why this is a significant step beyond previous methods to automate aspheric production, and how it has resulted in a generalized, scaleable technology that does not require high capital-value tooling customized to particular types of optical form. We summarise implementation in the first two automated CNC machines of 200 mm capacity, followed by the first 600 mm machine, and the current status of the process-development programme. We review quantitative results of polishing trials, including materials relevant to large and instrumentation optics. Finally, we comment on the potential of the technology for space optics and for removing quilting in honeycomb substrates.