Abstract Monte Carlo simulation of MRI signals is a powerful tool for modelling and quantifying tissue microstructure. While these methods have been used in MRI for decades, they typically focus on one aspect of microstructure and one type of MRI contrast at a time. In this paper, we present a new Monte Carlo MRI (MCMR) simulator for investigating the impact of tissue microstructure on arbitrary MRI sequences. A key feature of the proposed simulator is that substrates can incorporate multiple microstructural features (diffusion, T1/T2 relaxation, membrane permeability, local off-resonance fields, surface relaxation and magnetisation transfer) simultaneously. This provides a single forward model from tissue microstructure to MRI signals that captures a broad range of contrasts typically considered to be of different MRI “modalities”. We validate the results of the simulator by reproducing previous findings in well-established sequences, namely diffusion-weighted MRI, magnetisation transfer imaging, and gradient and spin echo sequences. The simulator is fully open source and packaged along with detailed documentation and tutorials.