High-energy neutron scattering measurements on the insulating pyrochlore magnet Ce₂Zr₂O₇ reveal that its Ce³⁺ pseudospin-1/2 degrees of freedom possess dipole-octupole character, making Ce₂Zr₂O₇ a candidate for novel quantum spin ice ground states at low temperature.  Muon spin relaxation measurements on single crystal Ce₂Zr₂O₇ show a lack of both magnetic order and spin freezing down to T = 0.02 K. Furthermore, low-energy inelastic neutron scattering measurements at low temperature show a lack of magnetic order and a snowflake-like pattern of diffuse scattering that is characteristic of quantum spin ice.  No obvious spin waves are observed in the low-energy excitation spectrum of Ce₂Zr₂O₇, in both zero and non-zero magnetic field, and this eliminates the most common method of estimating the microscopic spin Hamiltonian by fitting spin wave dispersions using linear spin wave theory. Instead, we use heat capacity, magnetic susceptibility, and diffuse neutron scattering measurements on Ce₂Zr₂O₇, combined with theoretical results from numerical linked cluster calculations, in order to estimate the terms in the nearest-neighbor exchange Hamiltonian expected for Ce₂Zr₂O₇. Polarized neutron diffraction measurements reveal zone-boundary diffuse scattering in the non-spin-flip channel which is not predicted by the nearest-neighbor Hamiltonian, and which we tentatively attributed to weak interactions beyond nearest neighbors. Finally, our in-field neutron scattering measurements show that magnetic fields along the [1,-1,0] and [0, 0, 1] directions induce partially-polarized and polarized spin ice phases at low temperatures, respectively, with the partially-polarized spin ice phase being particularly interesting due to the presence of field-decoupled, quasi-one-dimensional quantum spin chains within this phase. Altogether, our low-temperature characterization of Ce₂Zr₂O₇ makes a strong case for a pure quantum spin ice ground state in zero magnetic field, and sheds light on the exotic field-induced magnetic behaviour in Ce₂Zr₂O₇ for two magnetic field directions.