Ultrasound speckle is a consequence of the stochastic nature of the reflectivity of scattering media (e.g., biological tissue) and of the coherent nature of piezoelectric transducers. This speckle noise can be reduced by the use of incoherent processing techniques (e.g., spatial compounding, incoherent summation, random phase and phase insensitive transducers). We present a unified framework that explains the limitations of incoherent processing in terms of the information grain theory. This theory predicts the gains in SNR as well as the losses in directivity. We also present the random phase transducer approach to incoherence to total coherence. We present applications to speckle reduction, detection of specular reflectors, attenuation estimation and ultrasound imaging. We show that totally incoherent transducers completely remove diffraction effects. They might be used in attenuation estimation, in which case, correction for diffraction is no longer required, in order to obtain unbiased estimates. Partially coherent transducers might also be useful in imaging to reduce speckle noise.