Valley Hall effect is an appearance of the valley current in the direction transverse to the electric current. We develop the microscopic theory of the valley Hall effect in two-dimensional semiconductors where the electrons are dragged by the phonons or photons. We derive and analyze all relevant contributions to the valley current including the skew-scattering effects together with the anomalous contributions caused by the side jumps and the anomalous velocity. The partial compensation of the anomalous contributions is studied in detail. The role of two-phonon and two-impurity scattering processes is analyzed. We also compare the valley Hall effect under the drag conditions and the valley Hall effect caused by the external static electric field.