Diffusion Magnetic Resonance Imaging (dMRI) has been widely used to investigate human brain microstructure and connectivity and its abnormalities in a variety of brain deficits, whether acute, neurodevelopmental or neurodegenerative. However, the biological interpretation and validation of dMRI data modelling is still a crucial challenge in the field. In this respect, achieving high spatial resolution in-vivo dMRI in the non-human primate to compare these observations both with human dMRI on the one hand and 'ground truth' microstructural and histological data on the other hand is of outmost importance. Here, we developed a dMRI pulse sequence based on 3D-multishot Echo Planar Imaging (3D-msEPI) on a 3T human clinical scanner. We demonstrate the feasibility of cerebral dMRI at an isotropic resolution of 0.5 mm in 4 anesthetized macaque monkeys. The added value of the high-resolution dMRI is illustrated by focusing on two aspects. First, we show an enhanced descriptive power of the fine substructure of the hippocampus. Second, we show a more physiological description of the interface between cortex grey matter, superficial and deep white matter. Overall, the high spatial resolution dMRI acquisition method proposed in this study is a significant achievement with respect to the state of the art of dMRI on anesthetized monkeys. This study highlights also the potential of very high-resolution dMRI to precisely capture the microstructure of thin cerebral structures such as the hippocampus and superficial white matter.