Cosmic magnetism has that exotic ''Je ne sais quoi''! Magnetism has been observed in various objects, located near the edge of the Universe and all the way down to the Milky Way's center. The observed magnetic field can take the cell-type shape in randomly-oriented large blobs found in intracluster gas or outside of clusters of galaxies, the helix shape in synchrotron jets, the longitudinal shape in ram-pressured shocks in radio lobes near elliptical galaxies, the spiral shape of logarithmic arms in spiral galaxies, or the egg shape of an enlarged interstellar bubble. In strength, the magnetic field varies from 0.1 nG (cosmological), to 20 μG (galaxies, jets, superbubbles), and to 1 mG in the Milky Way filaments.Magnetism plays a small physical role in the formation of large structures. It acts as a tracer of the dynamical histories of cosmological and intracluster events, it guides the motion of the interstellar ionised gas, and it aligns the charged dust particles. Batteries and dynamos are often employed in models to create and amplify seed magnetic fields. Starting soon after the Big Bang (redshift z>2000), this review covers the cosmological background surface (z~1100, distance ~4.3 Gpc), the epoch of first stars (z~20; distance ~4.1 Gpc), the currently observable Universe (z~10, distance ~3.9 Gpc), superclusters of galaxies (size ~50 Mpc), intracluster gas (size ~10 Mpc), galaxies (~30 kpc), spiral arms (~10 kpc), interstellar superbubbles (~100 pc), synchrotron filaments (~10 pc), and the Milky Way's center.