Financial crime represents a growing issue which contemporary society is facing, especially in the form of money laundering, which aims to conceal the origin of illicit funds through a network of intermediate transactions. State of the art solutions for detection of money laundering in graph representations of financial data include supervised techniques such as Graph Neural Networks. Although provably efficient, their main limitation stands in the fact that they require a dataset of correctly and completely labeled transactions, which is often unfeasible to obtain. This work aims to explore money flow statistics as an unsupervised approach to money laundering detection, through computing statistics of accounts based on the amount of money received and sent in a certain time frame or network flow analysis using maximum flow algorithms. Therefore, this paper aims to answer two questions, namely What are the existing solutions using money flow statistics? and How would these money flow statistics methods perform on a realistic dataset of transactions?. The analysis benchmarks the identified algorithms on a realistic dataset of financial transactions in order to observe their limitations and suggest further research into how these limitations can be overcome in order to make money flow statistics methods a feasible solution to money laundering detection.