TIGRE is a MATLAB and Python/CUDA toolbox for fast and accurate 3D tomographic reconstruction (any geometry), created jointly by University of Bath’s Engineering Tomography Lab and CERN. The aim of TIGRE is to provide a wide range of easy-to-use iterative algorithms to the tomographic research community. The toolbox uses advanced iterative and regularized reconstruction methods. It can work with a wide variety of iterative algorithms, including Feldkamp-Davis-Kress (FDK) algorithms, simultaneous algebraic reconstruction technique (SART) algorithms and Krylov subspace algorithms. It also supports GPU-accelerated projection and back projection and covers a range of methods using total variation (TV) regularization with a modular design to better accommodate new algorithms.