The reasons for the creation of Illiac IV are described and the history of the Illiac IV project is recounted. The architecture or hard-ware structure of the Illiac IV is discussed--the Illiac IV array is an array processor with a specialized control unit (CU) that can be viewed as a small stand-alone computer. The Illiac IV software strategy is described in terms of current user habits and needs. Brief descriptions are given of the systems software itself, its history, and the major lessons learned during its development. Some ideas for future development are suggested. Applications of Illiac IV are discussed in terms of evaluating the function f(x) simultaneously on up to 64 distinct argument sets xi. Many of the time-consuming problems in scientific computation involve repeated evaluation of the same function on different argument sots. The argument sets which compose the problem data base must be structured in such a fashion that they can be distributed among 64 separate memories. Two matrix applications: Jacobi's algorithm for finding the eigenvalues and eigenvectors of real symmetric matrices, and reducing a real nonsymmetric matrix to the upper-Hessenberg form using Householder's transformations are discussed in detail. The ARPA network, a highly sophisticated and wide ranging experiment in the remote access and sharing of computer resources, is briefly described and its current status discussed. Many researchers located about the country who will use Illiac IV in solving problems will do so via the network. The various systems, hardware, and procedures they will use is discussed.