The BBC has a great intro article about how scientists, including those in the IPCC, model climate change. As scientific understanding and computing power have increased, scientists have been able to model more of the climate. The article includes a cool graphical evolution of climate modeling.
Key challenges for future models include making the models more accurate at the regional level, allowing them to adapt to regional data, and to study variations within weather systems.
Interestingly, the overall conclusions about the magnitude of global warming have not changed much over the past 20-30 years – only the statistical confidence in these numbers has!