The rise of digital payments has caused consequential changes in the financial crime landscape. As a result, traditional fraud detection approaches such as rule-based systems have largely become ineffective. AI and machine learning solutions using graph computing principles have gained significant interest in recent years. Graph-based techniques provide unique solution opportunities for financial crime detection. However, implementing such solutions at industrial-scale in real-time financial transaction processing systems has brought numerous application challenges to light. In this paper, we discuss the implementation difficulties current and next-generation graph solutions face. Furthermore, financial crime and digital payments trends indicate emerging challenges in the continued effectiveness of the detection techniques. We analyze the threat landscape and argue that it provides key insights for developing graph-based solutions.