The Compressive Sensing (CS) technique, first introduced in the field of image processing, is nowadays used in many engineering problems. Electromagnetics counts a number of problems which have been solved with a suitable CS-based strategy, such as, for examples, the diagnosis and synthesis of antenna arrays, the estimation of directions of arrival, and the solution of inverse scattering and radar imaging problems. This paper presents an overview of some algorithms based on the CS approach, recently developed by the authors for the synthesis of sparse antenna arrays, also including additional constraints.