The methods of detecting and measuring interstellar and intergalactic magnetic fields are reviewed and briefly discussed. Recent results are surveyed for magnetic fields in the Milky Way, its halo, galaxy halos, galaxy clusters, and the intergalactic medium. Preliminary evidence for the magnetic field strength in the circumgalactic halo of our galaxy is discussed, and suggests that there are significant contrasts in magnetic field strength in and around galaxies such as ours, and between galaxy clusters and the general intergalactic medium. The general trend of recent results indicates that, wherever we detect intergalactic hot gas and galaxies, we also find magnetic fields at levels of ≈10−7 G, or higher. The hitherto undetected, weaker fields in the general intergalactic medium outside of clusters and in large intergalactic voids might, in future, be measurable through observations of γ-rays and/or cosmic ray nuclei. There appear to be close, though so far incompletely understood connections between ult...