We discuss the evolution of the magnetic field of an accreting white dwarf. We calculate the ohmic decay modes for accreting white dwarfs, the interiors of which are maintained in a liquid state by compressional heating. We show that the lowest-order ohmic decay time is (8–12)×109 yr for a dipole field, and (4–6)×109 yr for a quadrupole field. We then compare the time-scales for ohmic diffusion and accretion at different depths in the star, and for a simplified field structure and assuming spherical accretion, study the time-dependent evolution of the global magnetic field at different accretion rates. We neglect mass loss by classical nova explosions and assume that the white dwarf mass increases with time. In this case, the field structure in the outer layers of the white dwarf is modified significantly for accretion rates above the critical rate M˙c≈(1–5)×10-10 M⊙ yr-1. We consider the implications of our results for observed systems. We propose that accretion-induced magnetic field changes are the missing evolutionary link between AM Her systems and intermediate polars. The shorter ohmic decay time for accreting white dwarfs provides a partial explanation of the lack of accreting systems with ≈109 G fields. In rapidly accreting systems such as supersoft X-ray sources, amplification of internal fields by compression may be important for type Ia supernova ignition and explosion. Finally, spreading matter in the polar cap may induce complexity in the surface magnetic field, and explain why the more strongly accreting pole in AM Her systems has a weaker field. We conclude with speculations concerning the field evolution when classical nova explosions cause the white dwarf mass to decrease with time.