- Compressive sensing provides a new framework for simultaneous sampling and compression of signals. According to compressive sensing theory one can recover compressible signals and images from far fewer samples or measurements that traditional methods use. Applying compressive sensing theory for holography comes natural since three-dimensional (3D) data is typically very redundant, thus it is also very compressible. Holographic imaging itself is inherently a compressive process that encodes 3D data in 2D images. The application of compressive sensing for holography may reduce the acquisition effort in terms of acquisition time and hardware; it reduces the overall captured data thus reducing storage requirements and transmission bandwidth. We present a survey of compressive sensing techniques proposed for coherent and incoherent holography. We also present theoretical results that provide applicative practical rules for using of compressive sensing theory in holography.