Magnetic susceptibility, specific heat, and resistivity measurements by Fisk et al. have revealed two ordering transitions in HoB4 at temperatures near 7.1 and 5.7 K. Moreover, the macroscopic measurements indicate that the higher temperature transition is of second order, the lower one of first order. Neutron diffraction measurements on polycrystalline and on single crystal specimens have confirmed these results. The magnetic scattering data have so far resisted a complete interpretation; the following conclusions can, however, be drawn. The magnetic structure in the high temperature phase has a strong oscillatory component, the wave vector of which is equal to (±0.021,±0.021, 0.425) in units of the reciprocal lattice vectors. The magnetic moments are parallel, in sheets normal to the tetragonal c-axis, to one of the four equivalent [100] reciprocal lattice directions. In the low-temperature phase there is a large component of the moments arranged in the simple colinear structure that has been reported for ErB4 and DyB4 by W. Schafer et al. In both temperature ranges there are additional, unexplained, magnetically scattered intensities. The magnetic phase diagram has been studied in applied fields up to 6.4 T and at temperatures down to 1.8 K. Polarization analysis and classical polarized beam techniques have been applied to the single crystals in selected field and temperature ranges.