Because they consume energy to drive their motion, systems of active colloids are intrinsically out of equilibrium. In past decades, a variety of intriguing dynamic patterns have been observed in systems of active colloids, which offer a new platform for studying non‐equilibrium physics, in which computer simulation and analytical theory have played an important role. Recent progress in understanding the dynamic assembly of active colloids by using numerical and analytical tools is reviewed, including progress in understanding the motility induced phase separation in the past decade, followed by discussion on the effect of shape anisotropy and hydrodynamics on the dynamic assembly of active colloids.