Graph analytics, a powerful tool for handling complex data, finds successful applications in industries such as pharmaceuticals, maritime routing, insurance, and social media. Financial crime detection particularly benefits from this technology by unraveling the intricacies of cash flow relationships among entities. However, organizations must understand the proper techniques to meet their evolving needs. Two main techniques—entity resolution and network filtering—have great strengths and benefit different situations depending on the business problem and data complexity. Entity resolution de-duplicates data records, while network filtering removes superfluous connections, important for financial institutions with multiple customer and transaction management systems. Real datasets often show imperfections, leading to weaker matches, but techniques like graph representation learning (GRL) address these challenges. GRL, a deep-learning technique, analyzes transaction graphs by learning important structural information. Popular algorithms like GraphSAGE improve accuracy in financial crime detection. Overcoming challenges such as over-smoothing, hardware requirements, and interpretability is crucial for maximizing the benefits of graph analytics. Organizations must consider their business profile, relationship complexities, and investigative user journey to improve investigation efficiency and detection sophistication. Understanding and adopting the right combination of techniques can lead to more effective anti-money laundering programs and enhanced customer experiences.