It is now well established that stellar winds of hot stars are fragmentary and that the X-ray emission from stellar winds has a strong contribution from shocks in winds. Chandra high spectral resolution observations of line profiles of O and B stars have shown numerous properties that had not been expected. Here we suggest explanations by considering the X-rays as arising from bow shocks that occur where the stellar wind impacts on spherical clumps in the winds. We use an accurate and stable numerical hydrodynamic code to obtain steady state physical conditions for the temperature and density structure in a bow shock. We use these solutions plus analytic approximations to interpret some major X-ray features: the simple power-law distribution of the observed emission measure derived from many hot star X-ray spectra and the wide range of ionization stages that appear to be present in X-ray sources throughout the winds. Also associated with the adiabatic cooling of the gas around a clump is a significant transverse velocity for the hot plasma flow around the clumps, and this can help to understand anomalies associated with observed line widths, and the differences in widths seen in stars with high and low mass-loss rates. The differences between bow shocks and the planar shocks that are often used for hot stars are discussed. We introduce an ‘‘on the shock’’ approximation that is useful for interpreting the X-rays and the consequences of clumps in hot star winds and elsewhere in astronomy.