The main purpose of this review is to present the statistical properties of dynamic speckle produced by a diffuse object that moves with a constant velocity and the velocimetry applications that result from these properties. In this way the space-time correlation function of the speckle intensity variation is examined. Two typical speckle motions: boiling and translation are identified and discussed for various optical configurations in the diffraction and image fields in the case of the in plane object motion. The following measurement methods for the diffuse object velocity are introduced: the autocorrelation method, cross-correlation method, spatial filtering method, and zero-crossing method. There are several versions of the above mentioned methods. Special attention is paid to those which allow us to measure both the magnitude and direction of the velocity. In the vast majority of methods the Gaussian illuminating beam is used. In this review the TEM10 illuminating beam is also taken into consideration. Then the autocorrelation methods of velocity measurement for the case of longitudinal motion are presented. It is shown that for this particular case the moving object need not to be a diffuse one, it can be a reflecting object as well. Possibility of the measurement of velocity which is arbitrarily directed with respect to the axis of the illuminating beam is also discussed. The speckle velocimetry methods in which the velocity is determined by means of a direct tracking and recording of the translating speckle generated by the moving object are mentioned. Finally some measurement systems in which laser speckles are used to evaluate subcutaneous flow of liquids are presented. Such systems were found useful in food conservation and medicine.