In this presentation, I discuss new simulation algorithms for the Heston model, which are based on recent results which show that the Heston model presents explicit weak solutions that can be used for simulating volatilities and prices. Most often, efficient simulation is done under an artificial reference probability and then converted to the real probability with the appropriate likelihood. The resulting simulation algorithm can therefore be seen as the analog of a weighted particle filter. It is then natural to introduce some type of resampling to improve the performance of the simulation algorithm. Here we focus on recently developed branching algorithms, which have the advantage of preserving the historical property of the particle system. Through numerical results, we illustrate the increased performance and accuracy due to branching. We also compare the resulting simulation algorithm to popular Heston simulation methods.