A microscopic statistical theory of homopolymer and copolymer melts in an electric field is developed. The nonlinear dielectric properties of a homopolymer melt in an electric field are described, the dipole-dipole interaction between the monomers being taken self-consistently into account. For diblocks, the order-disorder transition is studied in the framework of the random phase approximation. We predict that copolymer melts reveal four different universal types of behavior under external fields : A, B, C, and D. To determine what class a copolymer melt belongs to, the only relevant parameters turn out to be : f, the fraction of monomers A in a chain, and parameters S-(A) and S-(B), which characterize how many times the radii of gyration of blocks A and B increase, respectively, along an applied electric field. Class A represents strongly degenerated-in-electric-field copolymers, for which the anisotropic parts of the monomer A and B polarizabilities are equal. Near the spinodal point, X-ray scattering should reveal that critical wave vectors form an ellipsoid. After microphase separation, mesophases with nonfixed periodicity (which depends upon the direction of the symmetry breaking with respect to an electric field) appear. With increasing N-chi, these mesophases are three-dimensional triclinic, two-dimensional monoclinic, and one-dimensional lamellar structures. If the pattern appears spontaneously oriented along the electric field, the first two structures are body-centered tetragonal and honeycomb (hexagonal) structures, respectively. The spinodal line and lines of first-order transitions between mesophases are predicted to not depend on the electric field and coincide with those for zero electric field. For class B X-ray scattering should reveal that critical fluctuations are concentrated in and-space on two rings, which are perpendicular to the electric field. The temperature of the transition does not depend on the electric field but is different from that for zero electric field (only if f not equal 0.5). For a given composition f and an applied field, the angle between the field and the normal to the lamellar layers is fixed (does not depend on N-chi). For any composition f, a second-order transition occurs from a disordered melt to a lamellar phase without intermediate structures. For class C, only fluctuations oriented strictly along the electric field diverge at the spinodal point. For any composition f, a lamellar phase oriented perpendicularly to the electric field appears by a second-order transition from a homogeneous melt. The transition temperature and the pattern periodicity do depend on the electric field. For class D in Q-space, critical wave vectors form a ring perpendicularly to the electric field. For any composition f with increasing N-chi, a two-dimensional honeycomb and a lamellar structure oriented strictly parallel to the electric field appear by first-order transitions. The transition temperatures and the pattern periodicity depend on the applied field. In symmetric copolymers, reentrant disorder - order - disorder microphase transitions and orientational and reorientational phase transitions should be observed with an increase of the electric field intensity. Experimentally observable consequences, crucial for verification of the theory, and possible applications are discussed.