The global financial crisis of 2008 has led to the increased scrutiny of governance and conduct of financial services firms. A key component of monitoring conduct within this area is Financial Services Compliance Management. Financial institutions need to adhere to legislation such as the European MiFID II and GDPR through to anti-money laundering compliance. A recent report by Thomson Routers in 2018 has found through a survey with 800 financial firms that 66% of firms expect the cost of senior compliance staff to increase, up from 60% of firms in 2017, indicating a continuing growth in spending on compliance. Effective solutions need to be in place to mitigate these increasing costs while enhancing the compliance workflow. Doing this would provide a market edge. Artificial intelligence (AI) and machine learning (ML) have been gaining traction within the compliance management domain from both regulators and financial institutions in areas such as trade and market surveillance to regulatory compliance assurance. These areas share a commonality in terms of the volume of data to monitor often in real-time and from disparate sources both structured and unstructured with an emphasis on ensuring data quality and handling underlying bias in data. In this paper, an overview of the key use case areas of AI and ML in the compliance management domain will be provided. Detailed analysis on the application of specific AI solutions such as natural language processing, data discovery and generative modelling is introduced.