This document describes the EXOSIMS framework for simulating exoplanet direct imaging missions. EXOSIMS integrates independent modules that perform specific tasks into a unified mission simulation. Key modules include: Planet Population (generates planetary system parameters), Optical System (models telescope performance), Survey Simulation (runs observations), and Post-Processing (determines detections and yields). EXOSIMS has been used to model the science yield of the WFIRST-AFTA mission and provides an open-source tool for studying various mission designs.