Delay differential equations(DDEs) provide powerful and rich mathematical models that have been proven to be useful in simulating some real life problems. The current publicly available DDE solvers are either very formidable to use (especially for new users) or designed to support only selected classes of problems.In this thesis we have developed a new Fortran 90 DDE solver DDVERK90 that aims to combine the effectiveness of the Fortran 77 DDE solver DDVERK and the user-friendliness of the MATLAB ODE solvers. We have added the capability of embedded event location to facilitate many tasks that arise in applications. We have also introduced a new approach for classifying DDE problems that helps users to write driver programs to solve their problem very quickly. They do this by comparing their problem to other previously solved example problems in the same class and using the corresponding 'template' driver as a guide.