Federated Learning (FL) has emerged as a promising solution to address the limitations of centralised machine learning (ML) in oncology, particularly in overcoming privacy concerns and harnessing the power of diverse, multi-center data. This systematic review synthesises current knowledge on the state-of-the-art FL in oncology, focusing on breast, lung, and prostate cancer. Distinct from previous surveys, our comprehensive review critically evaluates the real-world implementation and impact of FL on cancer care, demonstrating its effectiveness in enhancing ML generalisability, performance and data privacy in clinical settings and data. We evaluated state-of-the-art advances in FL, demonstrating its growing adoption amid tightening data privacy regulations. FL outperformed centralised ML in 15 out of the 25 studies reviewed, spanning diverse ML models and clinical applications, and facilitating integration of multi-modal information for precision medicine. Despite the current challenges identified in reproducibility, standardisation and methodology across studies, the demonstrable benefits of FL in harnessing real-world data and addressing clinical needs highlight its significant potential for advancing cancer research. We propose that future research should focus on addressing these limitations and investigating further advanced FL methods, to fully harness data diversity and realise the transformative power of cutting-edge FL in cancer care.