Magnetohydrodynamical (MHD) turbulence is ubiquitous in magnetized astrophysical plasmas, and it radically changes a great variety of astrophysical processes. In this review, we introduce the concept of MHD turbulence and explain the origin of its scaling. We consider the implications of MHD turbulence for various problems: dynamo in different types of stars, flare activity, solar and stellar wind from different stars, the propagation of cosmic rays, and star formation. We also discuss how the properties of MHD turbulence provide a new means of tracing magnetic fields in interstellar and intracluster media.