MRI-guided intervention for the liver and kidney has achieved considerable progress in tumour diagnosis and treatment over the past two decades. However, due to the space constraints associated with the narrow and deep bore of the MRI machines, it is still extremely challenging for clinicians to position and drive the needle-shaped probes used for delivering the treatment where the targeted tumoral mass is located. MRIcompatible robotic systems have been investigated by several research teams worldwide, both in academia and industry. These endeavours aim to address challenges related to the confined workspace within MRI machine bores. The goal is to facilitate the shift from CT-guided to MRI-guided interventions, leveraging the advantages of MRI, including its exceptional soft tissue contrast, non-ionizing radiation, and versatile multi-angle imaging capabilities. In this article, we systematically review the state-of-the-art MRI-guided needle insertion robots for the treatment of the liver and kidney in order to identify challenges, trends and potential research gaps in this field.