The frustrated pyrochlore magnet Yb2Ti2O7 has the remarkable property that it orders magnetically, but has no propagating magnons over wide regions of the Brillouin zone. Here we use inelastic neutron scattering to follow how the spectrum evolves in cubic-axis magnetic fields. At high fields we observe in addition to dispersive magnons also a two-magnon continuum, which grows in intensity upon reducing the field and overlaps with the one-magnon states at intermediate fields leading to strong renormalization of the dispersion relations, and magnon decays. Using heat capacity measurements we find that the low and high field regions are smoothly connected with no sharp phase transition, with the spin gap increasing monotonically in field. Through fits to an extensive data set we re-evaluate the spin Hamiltonian finding dominant quantum exchange terms, which we propose are responsible for the anomalously strong fluctuations and quasiparticle breakdown effects observed at low fields. The lattice of corner-shared tetrahedra realized in cubic A 2 B 2 O 7 pyrochlores and AB 2 O 4 spinels, is a canonical lattice to explore correlated magnetism in the presence of strong geometric frustration effects. In the strongly spin-orbit coupled rare earth pyrochlores, experiment has uncovered materials offering a tremendously rich spectrum of magnetic behavior. Notable examples include classical spin ice physics as in the rare-earth titanates (Ho/Dy) 2 Ti 2 O 7 where Ising antiferromagnetism leads to an emergent classical electrostatics at low temperatures [1] and "order-by-disorder" in XY antiferromagnets where thermal and quantum fluctuations lift a large frustration-induced degeneracy resulting in unconventional magnetic order as in Er 2 Ti 2 O 7 [2-5]. Currently, much of the interest in this field concentrates on a handful of materials that seem to fall outside a semiclassical understanding of these systems. The pyrochlore Yb 2 Ti 2 O 7 [6-25], where Kramers Yb 3+ ions behave as effective spin 1/2 moments, is quite unique in its behavior: in high applied magnetic fields dispersive magnons were observed [12], which are apparently replaced by a broad continuum of scattering at zero field [16] despite the presence of ferromagnetic order. This exotic behavior is not yet understood. To make progress one would like to know i) how the broad scattering continuum in zero field originates from quantum fluctuations, whether those fluctuations are also present at high field and, if so, how they manifest themselves, ii) how the sharp magnons "disappear" over a wide range of the Brillouin zone as the field is lowered. Here we experimentally answer those questions by studying the behavior in a magnetic field applied along the cubic [001] direction, which has not been explored in detail before and which, we will show, allows for a transparent interpretation of the phase diagram and evolution of the spectrum in a magnetic field. The experiment also allows us to re-visit the parametrization of the magnetic exchange, which is a critical ingredien...