In recent years, the unprecedented growth in digital payments fueled consequential changes in fraud and financial crimes. In this new landscape, traditional fraud detection approaches such as rule-based engines have largely become ineffective. AI and machine learning solutions using graph computing principles have gained significant interest. Graph neural networks and emerging adaptive solutions provide compelling opportunities for the future of fraud and financial crime detection. However, implementing the graph-based solutions in financial transaction processing systems has brought numerous obstacles and application considerations to light. In this paper, we overview the latest trends in the financial crimes landscape and discuss the implementation difficulties current and emerging graph solutions face. We argue that the application demands and implementation challenges provide key insights in developing effective solutions.