MOTIVATION: Sequence simulations along phylogenetic trees play an important role in numerous molecular evolution studies such as benchmarking algorithms for ancestral sequence reconstruction, multiple sequence alignment, and phylogeny inference. They are also used in phylogenetic model-selection tasks, including the inference of selective forces. Recently, Approximate Bayesian Computation (ABC)-based approaches have been developed for inferring parameters of complex evolutionary models, which rely on massive generation of simulated data. For all these applications, computationally efficient sequence simulators are essential. RESULTS: In this study, we investigate fast algorithms for simulating sequences along a phylogenetic tree, focusing on accelerating the speed-limiting component of the simulation process: handling insertion and deletion (indel) events. We demonstrate that data structures which efficiently store indel events along a tree can substantially accelerate the simulation process compared to a naive approach. To illustrate the utility of this efficient simulator, we integrated it into an ABC-based algorithm for inferring indel model parameters and applied it to study indel dynamics within Chiroptera. AVAILABILITY AND IMPLEMENTATION: The source code for the different simulation algorithms, alongside the data used, is available at: https://github.com/nimrodSerokTAU/evo-sim. The simulator has also been integrated into SpartaABC, a website for the inference of indel parameters, accessible at: https://spartaabc.tau.ac.il/.