There is an increasing demand for evolutionary models to incorporate relatively realistic dynamics, ranging from selection at many genomic sites to complex demography, population structure, and ecological interactions. Such models can generally be implemented as individual‐based forward simulations, but the large computational overhead of these models often makes simulation of whole chromosome sequences in large populations infeasible. This situation presents an important obstacle to the field that requires conceptual advances to overcome. The recently developed tree‐sequence recording method (Kelleher, Thornton, Ashander, & Ralph, 2018), which stores the genealogical history of all genomes in the simulated population, could provide such an advance. This method has several benefits: (1) it allows neutral mutations to be omitted entirely from forward‐time simulations and added later, thereby dramatically improving computational efficiency; (2) it allows neutral burn‐in to be constructed extremely efficiently after the fact, using “recapitation”; (3) it allows direct examination and analysis of the genealogical trees along the genome; and (4) it provides a compact representation of a population's genealogy that can be analysed in Python using the msprime package. We have implemented the tree‐sequence recording method in SLiM 3 (a free, open‐source evolutionary simulation software package) and extended it to allow the recording of non‐neutral mutations, greatly broadening the utility of this method. To demonstrate the versatility and performance of this approach, we showcase several practical applications that would have been beyond the reach of previously existing methods, opening up new horizons for the modelling and exploration of evolutionary processes.