MOCCT: A numerical technique for astrophysical MHD. Magnetic fields are important components of many astrophysical systems. These systems are studied with numerical simulations of the equations of magnetohydrodynamics (MHD). We briefly review the MHD assumptions, some of the numerical approaches currently in use, and some of the problems to which MHD codes are being applied. We describe in detail the Method of Characteristics-Constrained Transport scheme (MOCCT). This is a time-explicit, operator split, nonconservative technique that uses information propagated along Alfvén characteristics to compute electromagnetic forces at intermediate time levels for the induction equation and for the Lorentz force. The advantages and difficulties with this scheme are investigated with a series of test problems