One of the fundamental theorem in information theory is the so-called sampling theorem also known as Shannon-Nyquist theorem. This theorem aims at giving the minimal frequency needed to sample and reconstruct perfectly an analog band-limited signal. Compressive sensing (or compressed sensing, compressive sampling) or CS in short is a recent theory that allows, if the signal to be reconstructed satisfies a number of conditions, to decrease the amount of data needed to reconstruct the signal. As a result this theory can be used for at least two purposes: i) accelerate the acquisition rate without decreasing the reconstructed signal quality (e.g. in terms of resolution, SNR, contrast …) ii) improve the image quality without increasing the quantity of needed data. Even if medical ultrasound is a domain where several potential applications can be highlighted, the use of this theory is extremely recent. In this paper we will review the basic theory of compressive sensing. The concepts of sparsity and incoherence between decomposition and representation basis, which are necessary conditions for the CS to apply will be presented. Illustrations of the application of CS to other domains will be presented. A review of the existing CS studies in the field of medical ultrasound will be given: reconstruction of pre-beamformed data using CS, reconstruction of 3D ultrasound volumes using CS, bayesian approaches of CS in medical ultrasound, blood velocity estimation from sparse data sets using CS. Finally the open problems and challenges remaining to be tackled in order to make the application of CS to medical US a reality will be given.