Checking regulatory compliance of business processes prior to deployment is common practice and numerous approaches have been developed over the last decade. However, the computational complexity of the problem itself has never received any major attention. Although it is known that the complexity of the problem is generally in NP-complete, many existing approaches ignore the issue using the excuse that current problems are small enough to be solved anyway. However, due to the current race towards digitalisation and automatisation, the size and complexity of the problems is bound to increase. As such, this paper investigates the computational complexity of all sub-classes of the problem and categorises some of the existing approaches, providing a detailed overview of the issues that require to be tackled in order for current compliance checking solutions to remain feasible in future scenarios.