Ultrafast ultrasound (US) imaging based on plane wave (PW) insonification is a widely used modality nowadays. Two main types of approaches have been proposed for image reconstruction either based on classical delay-and-sum (DAS) or on Fourier reconstruction. Using a single PW, these methods lead to a lower image quality than DAS with multi-focused beams. In this paper we review recent beamforming approaches based on sparse regularization methods. The imaging problem, either spatial-based (DAS) or Fourier-based, is formulated as a linear inverse problem and convex optimization algorithms coupled with sparsity priors are used to solve the ill-posed problem. We describe two applications of the framework namely the sparse inversion of the beamforming problem and the compressed beamforming in which the framework is combined with compressed sensing. Based on numerical simulations and experimental studies, we show the advantage of the proposed methods in terms of image quality compared to classical methods.