In radiology, phantoms are utilized to estimate radiation dose delivered to patients and evaluate the quality of imaging systems. Hence, the material of the phantoms should closely mimic the human tissue; in particular, the radiological characteristics of the material must be similar to that of the tissue. This article reviews materials used to manufacture phantoms for radiology applications. In the first section, basic physics relevant to the phantom material and radiation interaction with matter is discussed. A brief history of the phantom material for radiology is offered. The second section gives extensive discussion on the materials mainly developed by D.R.White, C.Constantinou, and co‐workers in late 1970s to early 1980s. Their materials were made based on epoxy resin. They produced tissue‐equivalent materials mimicking 15 different tissue types. Detailed description on manufacturing methods and the results of evaluation is presented. Since their seminal work other investigators developed tissue‐equivalent materials by using polyethylene and polyurethane as base. Short discussion on those newer developments is given. The third section presents, how those materials are used for radiation dosimetry, radiation therapy, and diagnostic radiology. Our discussion on applications will be limited to the phantoms used with photons and electrons since most medical applications utilize those particles. The last section is devoted to speculative discussion on what types of phantom and material will be developed in the near future.