Natural ice is formed by freezing of water or by sintering of dry or wet snow. Each of these processes causes atmospheric air to be enclosed in ice as bubbles. The air amount and composition as well as the bubble sizes and density depend not only on the kind of process but also on several environmental conditions. The ice in the deepest layers of the Greenland and the Antarctic ice sheet was formed more than 100 000 years ago. In the bubbles of this ice, samples of atmospheric air from that time are preserved. The enclosure of air is discussed for each of the three processes. Of special interest are the parameters which control the amount and composition of the enclosed air. If the ice is formed by sintering of very cold dry snow, the air composition in the bubbles corresponds with good accuracy to the composition of atmospheric air.