  For both the FCC-ee and the ILC, to exploit properly the respective precision
physics program, the theoretical precision tag on the respective luminosity
will need to be improved from the analogs of the $ 0.054 \% (0.061\%)$ results
at LEP at $M_Z$, where the former (latter) LEP result has (does not have) the
pairs correction. At the FCC-ee at $M_Z$ one needs improvement to $0.01\%$, for
example. We present an overview of the roads one may take to reach the required
$0.01\%$ precision tag at the FCC-ee and of what the corresponding precision
expectations would be for the FCC-ee$_{350}$, ILC$_{500}$, ILC$_{1000}$, and
CLIC$_{3000}$ setups.
