Low Dose Rate Brachytherapy (LDR-BT) is a technique for treating localized prostate cancer by implanting radioactive seeds. In conventional practice, the delivery of seeds is performed using transrectal ultrasonography (TRUS) imaging for implant guidance and checked using computed-tomography for post-implant dosimetry. In the case of TRUS, accuracy can be compromised due to sub-optimal imaging. Magnetic Resonance Imaging (MRI), however, is known to provide better soft-tissue contrast, therefore, increasing the ability to detect small lesions; for that reason, the integration of intraoperative MRI in BT workflows has been investigated over the last two decades. The fusion of preoperative MR-images during TRUS-brachytherapy is possible. However, the image registration process introduces a source of uncertainty. Manual, real-time intra-operative LDR-BT is challenging under MRI due to confined space and procedural workflows. This motivates the development of MRI-compatible robots for prostate BT, with potential advantages of improved source placement accuracy and final dosimetry. In this paper, the state-of-art of technological components in MRI compatible robots, especially for LDR-BT, has been presented. This systematic review helps us to position an ongoing Cooperative Brachytherapy project, developing a real-time MRI-guided robot for adaptive LDR-BT. The design approach includes integrating separate modules: imaging, dose planning, needles, and robot.