The interplay between chirality and magnetic fields gives rise to a cross effect referred to as magnetochiral anisotropy (MChA), which can manifest itself in different physical properties of chiral magnetized materials. The first experimental demonstration of MChA was by optical means with visible light. Further optical manifestations of MChA have been evidenced across most of the electromagnetic spectrum, from terahertz to X-rays. Moreover, exploiting the versatility of molecular chemistry towards chiral magnetic systems, many efforts have been made to identify the microscopic origins of optical MChA, necessary to advance the effect towards technological applications. In parallel, the replacement of light by electric current has allowed the observation of non-reciprocal electrical charge transport in both molecular and inorganic conductors as a result of electrical magneto-chiral anisotropy (eMChA). MChA in other domains such as sound propagation and photo-and electro-chemistry are still in their infancy, with only a few experimental demonstrations, and offer wide perspectives for further studies with potentially large impact, like the understanding of the homochirality of life. After a general introduction to magneto-chiral anisotropy, we give a complete review of all these phenomena, particularly during the last decade.