With the increase in computational power in the last decade and the forthcoming Exascale supercomputers, a new horizon in computational modelling and simulation is envisioned in combustion science. Considering the multiscale and multiphysics characteristics of turbulent reacting flows, combustion simulations are considered as one of the most computationally demanding applications running on cutting-edge supercomputers. Exascale computing opens new frontiers for the simulation of combustion systems as more realistic conditions can be achieved with high-fidelity methods. However, an efficient use of these computing architectures requires methodologies that can exploit all levels of parallelism. The efficient utilization of the next generation of supercomputers needs to be considered from a global perspective, that is, involving physical modelling and numerical methods with methodologies based on High-Performance Computing (HPC) and hardware architectures. This review introduces recent developments in numerical methods for large-eddy simulations (LES) and direct-numerical simulations (DNS) to simulate combustion systems, with focus on the computational performance and algorithmic capabilities. Due to the broad scope, a first section is devoted to describe the fundamentals of turbulent combustion, which is followed by a general description of state-of-the-art computational strategies for solving these problems. These applications require advanced HPC approaches to exploit modern supercomputers, which is addressed in the third section. The increasing complexity of new computing architectures, with tightly coupled CPUs and GPUs, as well as high levels of parallelism, requires new parallel models and algorithms exposing the required level of concurrency. Advances in terms of dynamic load balancing, vectorization, GPU acceleration and mesh adaptation have permitted to achieve highly-efficient combustion simulations with data-driven methods in HPC environments. Therefore, dedicated sections covering the use of high-order methods for reacting flows, integration of detailed chemistry and two-phase flows are addressed. Final remarks and directions of future work are given at the end. }