We survey the range of techniques for numerical simulation of the beam‐beam interaction in circular colliders in which synchrotron radiation is present. These include techniques used in weak‐strong, quasi‐strong‐strong, and strong‐strong simulations. Self‐consistent strong‐strong simulations usually use macroparticle‐in‐cell methods with a variety of refinements to increase the computational speed. Other approaches include macroparticle sampling methods and numerical solution of the Vlasov equation. We also describe and compare the existing beam‐beam simulation codes for circular lepton colliders. © 2003 American Institute of Physics