The mapping of atomic arrangement by X-ray analysis, first applied only to crystalline solids, but more recently extended to amorphous solids, liquids, and gases, has now been pursued for more than twenty years. In the present paper an attempt is made to review the position which has been reached and to forecast the probable lines of development in the future. Examples are chosen from inorganic chemistry, organic chemistry, mineralogy, metallurgy, and biochemistry, which are as far as possible representative of the problems to which X-ray analysis can be effectively applied. It is perhaps not generally realised how extensive these applications are and how much they are influencing other branches of science. A knowledge of the actual atomic arrangement introduces an important precision, simplicity, and novelty of outlook, and a plea might well be made for a wider use of the new knowledge.