At the time when most of image data in hospitals are stored in digital form using picture archiving and communication systems (PACS), telemedicine goes through its boom, and demand for data storage and bandwidth requirements increases, lossy compression techniques become necessity. This review article summarizes different methods for quality measurement of image compression in radiology. After brief compression techniques description, technical and medical measurements (including Receiver Operating Characteristic Curves) of image compression are described. Employing of these methods in practice and their results are shown on sample studies. The article concludes with basic recommendations for experimental protocols when performing quality measurement of medical images.