This paper provides an overview of the unique modeling and simulation challenges and needs in the system and safety analysis of two common types of High Temperature Gas-cooled Reactor (HTGR) designs. The challenges are associated with the complex core geometry configurations and the change of the dominant heat removal mechanisms between normal operating conditions and decay heat removal transients. This requires that simulation tools utilize models with reasonable length scales and capture both the localized heat transfer and the core-scale heat transfer at the same time. To meet such analysis needs, different methodologies were developed. This includes adopting existing methods and further developing/improving them, as well as proposing innovative methods that leverage advanced computational frameworks such as the Multiphysics Object Oriented Simulation Environment (MOOSE).