The principal topic of the thesis is the design of computer systems which incorporate graphical interaction, and their representation as collections of communicating processes. Chapter 1 describes the author's contribution to the development of the graphics satellite concept, in particular the fixed function graphics satellite and the programmable graphics processor. The evolution of the SPINDLE graphics system is described, with particular emphasis on the novel interactive techniques it incorporated, and on the solutions it provided to the problems of graphical interaction where the application program is timeshared. In Chapter 2 the structuring of a graphics system as a pipeline of independent but communicating processes is discussed. The concepts of static and dynamic device independence are introduced, and the implementation is described of a system which permits dynamic device independence by the creation of new processes at run time. This system also shows how the use of standard device support libraries and a human-readable picture description format allows a post-processor for any device to be generated automatically from the support library and a BNF-like definition of the picture description syntax. The provision of simple graphical input by means of two-way communication between the component processes is also described. This work demonstrates the flexibility that can be achieved by the application of the "software tools" approach to graphics system design. Generalisation of the communicating processes model to allow for asynchronous graphical input and local response generation is the subject of Chapter 3. A synthesis of the ideas presented in the first two chapters leads to the concept of the programmable graphics multiprocessor (PGM) as a fundamental building block in a hierarchically structured graphics system. The proposed functions and properties of the PGM module are discussed in detail, and its relevance to a range of graphics systems is established. Chapter 4 reviews the growing field of interactive dialogue specification and user interface management systems, and suggests a parallel between dialogue structure and system structure. The hierarchical structuring of interactive dialogues is discussed, and the use of the PGM as a "graphical Shell" for the top-down design of graphical dialogues is described. Finally the further work needed towards a full implementation and application of the PGM model is indicated.