In this paper the main problems of the theory of the short-period geomagnetic secular variation are described. An approximate analytical representation of the observational data on both the geomagnetic field variations and the associated variations in the length of the day, the kinematics of the generation of geomagnetic variations in the skin-layer at the core-mantle boundary and the influence of the electrical conductivity of the mantle on the geomagnetic variations are considered. A theory of torsional oscillations in the Earth's core is developed and an attempt is made to evaluate the associated geomagnetic variations. Magnetohydrodynamic effects in a possible thin layer of stably stratified fluid near the core-mantle boundary are investigated.