Bank transactions are highly confidential. As a result, there are no real public data sets that can be used to investigate and compare anti-money laundering (AML) methods in banks. This severely limits research on important AML problems such as efficiency, effectiveness, class imbalance, concept drift, and interpretability. To address the issue, we present SynthAML: a synthetic data set to benchmark statistical and machine learning methods for AML. The data set builds on real data from Spar Nord, a systemically important Danish bank, and contains 20,000 AML alerts and over 16 million transactions. Experimental results indicate that performance on SynthAML can be transferred to the real world. As use cases, we present and discuss open problems in the AML literature.