The NEURON simulator has been developed over the past three decades and is widely used by neuroscientists to model the electrical activity of neuronal networks. Large network simulation projects using NEURON have supercomputer allocations that individually measure in the millions of core hours. Supercomputer centers are transitioning to next generation architectures and the work accomplished per core hour for these simulations could be improved by an order of magnitude if NEURON was able to better utilize those new hardware capabilities. In order to adapt NEURON to evolving computer architectures, the compute engine of the NEURON simulator has been extracted and has been optimized as a library called CoreNEURON. This paper presents the design, implementation, and optimizations of CoreNEURON. We describe how CoreNEURON can be used as a library with NEURON and then compare performance of different network models on multiple architectures including IBM BlueGene/Q, Intel Skylake, Intel MIC and NVIDIA GPU. We show how CoreNEURON can simulate existing NEURON network models with 4–7x less memory usage and 2–7x less execution time while maintaining binary result compatibility with NEURON.