The steady trend towards increased magnetic and geometric complexity in the design of accelerator magnets has caused a need for reliable 3D computer models and a better understanding of the behavior of magnetic system in three dimensions. The capabilities of the MAGNUS-3D family of programs are ideally suited to solve this class of problems and provide insight into 3D effects. MAGNUS-3D can solve any problem of magnetostatics involving permanent magnets, nonlinear ferromagnetic materials and electric conductors. MAGNUS-3D uses the finite element method and the two-scalar-potentials formulation of Maxwell's equations to obtain the solution, which can then be used interactively to obtain tables of field components at specified points or lines, plots of field lines, function graphs representing a field component plotted against a coordinate along any line in space (such as the beam line), and views of the conductors, the mesh and the magnetic bodies. The magnetic quantities that can be calculated include the force or torque on conductors or magnetic parts, the energy, the flux through a specified surface, line integrals of any field component along any line in space, and the average field or potential harmonic coefficients. We describe the programs with emphasis placed on their use for accelerator magnet design, and present an advanced example of actual calculations.