Neither the chiral limit nor finite baryon density can be simulated directly in lattice QCD,
which severely limits our understanding of the QCD phase diagram.
In this review I collect results for the phase structure in an extended parameter space
of QCD, with varying numbers of flavours, quark masses, colours, lattice spacings, imaginary and
isospin chemical potentials. Such studies help in understanding the underlying symmetries
and degrees of freedom, and are beginning to provide a consistent picture constraining the possibilities for the physical