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High-energy x-ray-diffraction experiments performed on rhombohedral $\mathrm{Pb}({\mathrm{Zn}}_{1/3}{\mathrm{Nb}}_{2/3}{)}_{1\ensuremath{-}x}{\mathrm{Ti}}_{x}{\mathrm{O}}_{3}$ $(\mathrm{PZN}\ensuremath{-}x%\mathrm{PT})$ crystals with $x=4.5%$ and 8% show that an electric field applied along the [001] direction induces the tetragonal phase, as proposed by Park and Shrout. Our experiments reveal that in PZN-4.5%PT such a phase change occurs via a third phase with monoclinic symmetry ${M}_{A},$ which is observed at intermediate field values. This is in agreement with first-principles calculations by Fu and Cohen predicting the rotation of the polarization between the rhombohedral and tetragonal phases in this material. A different polarization path between the rhombohedral and tetragonal phases, through a second monoclinic phase ${M}_{C},$ has been previously reported in PZN-8%PT. The microscopic characterization of these crystals allows us to explain the ultrahigh macroscopic strain observed in $\mathrm{PZN}\ensuremath{-}x%\mathrm{PT}$ under an electric field. Furthermore, some unusual scattering profiles displayed by exceptionally good crystals provide experimental evidence of the high anharmonicities and near degeneracy of the different phases in these extremely deformable materials.