Smart adaptive structures and structronic systems have been increasingly investigated and developed in the last two decades. Although smart structures made of piezoelectrics, shape-memory materials, electrostrictive materials, and electro-/magnetorheological fluids have been evaluated extensively, studies of magnetostrictive continua, especially generic mathematical model(s), are still relatively scarce. This study is to develop a generic mathematical model for adaptive and controllable magnetostrictive thin shells. Starting with fundamental constitutive magnetostrictive relations, both elastic and magnetostrictive stresses, forces, and moments of a generic double-curvature magnetostrictive shell continuum subject to small and moderate magnetic fields are defined. Dynamic magnetomechanical system equations and permissible boundary conditions are defined using Hamilton's principle, elasticity theory, Kirchhoff-Love thin shell theory and the Gibb's free energy function. Magnetomechanical behavior and dynamic characteristics of magnetostrictive shells are evaluated. Simplifications of magnetostrictive shell theory to other common geometries are demonstrated and magnetostrictive/dynamic coupling and actuation characteristics are discussed.