Compressed sensing (CS) aims to reconstruct signals and images from significantly fewer measurements than were traditionally thought necessary. In this paper, we propose a review of CS in biomedical imaging applications, along with a review of recent applications in the biomedical imaging field. The aim is to provide an analysis of the current trends in CS, focusing on the advantages and disadvantages in compressing biomedical imaging. One of the critical issue that used to hinder the application of compressed sensing in a biomedical imaging context is the computational cost of the underlying image reconstruction process. Furthermore, CS is compared to state-of-the-art compression algorithms in computed tomography (CT) and Magnetic Resonance Imaging (MRI) as examples of typical biomedical imaging. The main technical challenges associated with CS are discussed along with the predicted future trends.