The modeling and computational requirements to represent in detail various system elements and conditions to properly study stability in Microgrids (MGs) could be very onerous, requiring certain computational tools that restrict the types of studies that can be performed, thus limiting dynamic simulations to a few seconds for a reduced number of MG components. Moreover, model approximations that reduce computational burden and may be able to efficiently represent certain dynamic phenomena in MGs, might not be sufficient to fully analyze the stability of these systems. Therefore, this document focuses on studying and determining the validity and types of applications of detailed and approximate component models for MG dynamic studies and simulations, in the context of the IEEE 1547 standard, in particular generator and grid modeling, full and average converter models, unbalanced and balanced system conditions, dynamic and static loads,and detailed and simplified controls considering communications delays, packet losses, and security issues. A discussion of the use of phasor vis-à-vis electromagnetic transient simulation tools for dynamic stability studies is also presented,together with the role that dynamic phasor and co-simulation approaches could play in such studies. Considering the future integration of grids and MGs to form broad integrated networks, modeling scale-up issues as well as MG equivalent models,specifically white-, grey-, and black-box models,are discussed in the context of dynamic stability analysis and simulations of such largesystems. Finally, the modeling needs in MG protection are presented.