  In lattice QCD and other field theories with a mass gap, the field variables
in distant regions of a physically large lattice are only weakly correlated.
Accurate stochastic estimates of the expectation values of local observables
may therefore be obtained from a single representative field. Such master-field
simulations potentially allow very large lattices to be simulated, but require
various conceptual and technical issues to be addressed. In this talk, an
introduction to the subject is provided and some encouraging results of
master-field simulations of the SU(3) gauge theory are reported.
