Although 158Tb has recently been of interest in a proposed method for a determination of the neutrino rest mass, there was considerable confusion about the nuclear structure of this nuclide. The present work describes several charged-particle reaction studies which have been performed to clarify the nature of the low-lying levels, and to search for previously unknown ones. Angular distributions of the 159Tb(d, t)158 and 161Dy(p, α)158Tb reactions were measured with beam energies of 15 MeV and 17 MeV, respectively. Some spectra were also recorded for the 159Tb(3He, α)158Tb reaction at 28 MeV. Reaction products were analyzed with a magnetic spectrograph and detected with nuclear emulsions. Below ⋍ 400 keV in excitation energy the data are well explained by the Nilsson model, including Coriolis mixing, with a 32+[411] proton coupled to 32−, 52+[642] and 112−[505] neutrons. At higher energies other Nilsson orbitals for the odd proton become involved and configurations such as 52+[532]p ± 52+[642]n are observed. Also, there are many levels associated with 32+[402] and 12+[400] neutron orbitals coupled to a 32+[411] proton, but for which the fragmentation of strength indicates mixing of the configurations. No evidence was found for any low-lying (⋍20keV) isomeric state that might decay to the 1187 keV level in 158Gd. The present results confirm the interpretation of 158Tb levels that implies the electron capture decay of 158Tb is not particularly useful for a neutrino mass determination.