Arbor is a high-performance library for computational neuroscience simulations with multi-compartment, morphologically-detailed cells, from single cell models to very large networks. Arbor is written from the ground up with many-cpu and gpu architectures in mind, to help neuroscientists effectively use contemporary and future HPC systems to meet their simulation needs. Arbor supports NVIDIA and AMD GPUs as well as explicit vectorization on CPUs from Intel (AVX, AVX2 and AVX512) and ARM (Neon and SVE). When coupled with low memory overheads, this makes Arbor an order of magnitude faster than the most widely-used comparable simulation software. Arbor is open source and openly developed, and we use development practices such as unit testing, continuous integration, and validation.