Magnetohydrodynamics (MHD) studies the interaction between the flow of an electrically conducting fluid and magnetic fields. It involves such diverse topics as the evolution and dynamics of astrophysical objects, thermonuclear fusion, metallurgy and semiconductor crystal growth, etc. Although the first ideas in magnetohydrodynamics appeared at the beginning of the last century, the "explosion" in theoretical and experimental studies occurred in the 1950s-60s. This state-of-the-art book aims at revising the evolution of ideas in various branches of magnetohydrodynamics (astrophysics, earth and solar dynamos, plasmas, MHD turbulence and liquid metals) and reviews current trends and challenges.