The integrating sphere is a simple, yet often misunderstood device for measuring optical radiation. The function of an integrating sphere is to spatially integrate radiant flux. Before one can optimize a sphere design for a particular application, it is important to understand how the integrating sphere works. How light passes through the sphere begins with a discussion of diffuse reflecting surfaces. From this, the radiance of the inner surface of an integrating sphere is derived and two related sphere parameters are discussed, the sphere multiplier and the average reflectance. Finally, the time constant of an integrating sphere as presented is relevant to applications involving fast pulsed or short lived radiant energy.