This paper reviews the present state of knowledge concerning the diurnal and semidiurnal variations in the galactic cosmic ray intensity. The analytical procedures that are required for extracting from the original data the desired information concerning the characteristics of the anisotropies outside the magnetosphere are described. These include corrections for atmospheric fluctuations, the determination of the amplitudes and phases of the daily variations, and their interpretation in terms of the free space anisotropies that give rise to them. The experimental results concerning the 24-h wave, including its long-term variations with periods of one and two solar cycles, and the characteristics of the total dmrnal anisotropy are then discussed. The semidmrnal amsotropy is considered next. Transient anisotropies which manifest themselves as day-to-day variations, recurrence tendencies, cosmic ray storms, and diurnal variation trains, and which can introduce appreciable changes in the spectral parameters, are also of interest. The evolution of theoretical models developed to account for the diurnal and semidiurnal anisotropies, and fluctuations thereof, are then discussed in the light of the experimental results. Finally, the general features that are now well established, and the nature of the remaining problems, are summarized.