Evolutionary computation is an area within the field of artificial intelligence that is founded upon the principles of biological evolution. Evolution can be defined as the process of gradual development. Evolutionary algorithms are typically applied as a generic problem solving method, searching a problem space in order to locate good solutions. These solutions are found through an iterative evolutionary search that progresses by means of gradual developments. In the majority of cases of evolutionary computation the user is not aware of their algorithm's search behaviour. This causes two problems. First, the user has no way of assuring the quality of any solutions found other than to compare the solutions found by the algorithm with any available benchmark solutions or to re-run the algorithm and check if the results can be repeated or improved upon. Second, because the user is unaware of the algorithm's behaviour they have no way of identifying the contribution of the different components of the algorithm and therefore, no direct way of analyzing the algorithm's design and assigning credit to good algorithm components, or locating and improving ineffective algorithm components. The artificial intelligence and engineering communities have been slow to accept evolutionary computation as a robust problem-solving method because, unlike cased-based systems, rule-based systems or belief networks, they are unable to follow the algorithm's reasoning when locating a set of solutions in the problem space. During an evolutionary algorithm's execution the user may be able to see the results of the search but the search process itself like is a "black box" to the user. It is the search behaviour of evolutionary algorithms that needs to be understood by the user, in order for evolutionary computation to become more accepted within these communities. The aim of software visualization is to help people understand and use computer software. Software visualization technology has been applied successfully to illustrate a variety of heuristic search algorithms, programming languages and data structures. This thesis adopts software visualization as an approach for illustrating the search behaviour of evolutionary algorithms. Genetic Algorithms ("GAs") are used here as a specific case study to illustrate how software visualization may be applied to evolutionary computation. A set of visualization requirements are derived from the findings of a GA user study. A number of search space visualization techniques are examined for illustrating the search behaviour of a GA. "Henson," an extendable framework for developing visualization tools for genetic algorithms is presented. Finally, the application of the Henson framework is illustrated by the development of "Gonzo," a visualization tool designed to enable GA users to explore their algorithm's search behaviour. The contributions made in this thesis extend into the areas of software visualization, evolutionary computation and the psychology of programming. The GA user study presented here is the first and only known study of the working practices of GA users. The search space visualization techniques proposed here have never been applied in this domain before, and the resulting interactive visualizations provide the GA user with a previously unavailable insight into their algorithm's operation.