Nek5000 is a computational fluid dynamics code that employs the spectral element method, ahigh-order weighted residual technique, for applications in a wide range of fields including fluid flow, thermal convection, conjugate heat transfer, combustion and magnetohydrodynamics. It features state-of-the-art, scalable algorithms that are fast and efficient on platforms ranging from laptops to the world’s fastest computers. Nek5000, which is actively developed and improved for more than 30 years at Argonne National Laboratory (ANL), was extended for the direct numerical simulation of low Mach number reactive flows at the Swiss Federal Institute of Technology Zurich and is been used to investigate gas-phase and catalytic combustion in a number of laboratory-scale setups of fundamental and applied interest including internal combustion engines. Nek5000 won a Gordon Bell prize for its outstanding scalability on high-performance parallel computers and the 2016 R&D 100 Award. It is part of the Center for Efficient Exascale Discretizations (CEED) co-design effort, and its user community involves hundreds of scientists and engineers in academia, laboratories and industry.