We present powder and single-crystal neutron diffraction and bulk measurements of the Kagomé-staircase compound Ni3V2O8 (NVO) in fields up to 8.5T applied along the c direction. (The Kagomé plane is the a−c plane.) This system contains two types of Ni ions, which we call “spine” and “cross-tie.” Our neutron measurements can be described with the paramagnetic space group Cmca for T<15K and each observed magnetically ordered phase is characterized by the appropriate irreducible representation(s). Our zero-field measurements show that at TPH=9.1K NVO undergoes a transition to a predominantly longitudinal incommensurate structure in which the spine spins are nearly along the a-axis. At THL=6.3K, there is a transition to an elliptically polarized incommensurate structure with both spine and cross-tie moments in the a−b plane. At TLC=4K the system undergoes a first-order phase transition to a commensurate antiferromagnetic structure with the staggered magnetization primarily along the a-axis and a weak ferromagnetic moment along the c-axis. A specific heat anomaly at TCC′=2.3K indicates an additional transition, which remarkably does not affect Bragg peaks of the commensurate C structure. Neutron, specific heat, and magnetization measurements produce a comprehensive temperature-field phase diagram. The symmetries of the incommensurate magnetic phases are consistent with the observation that only one phase is electrically polarized. The magnetic structures are explained theoretically using a simplified model Hamiltonian, that involves competing nearest- and next-nearest-neighbor exchange interactions, single-ion anisotropy, pseudodipolar interactions, and Dzyaloshinskii-Moriya interactions.